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### Slope of Lines

- Slope = the ratio between the vertical rise and horizontal run
- The slope m of a line containing two points with coordinates (x
_{1}, y_{1}) and (x_{2}, y_{2}) is given by the formula - Slope postulates:
- Two non-vertical lines have the same slope if and only if they are parallel
- Two non-vertical lines are perpendicular if and only if the product of their slopes is -1

### Slope of Lines

- A(4, 3), B( − 4, 0)

- Graph the points on a coordinate plane

- slope of line p: m = [(9 − 3)/(5 − 2)] = [6/3] = 2
- slope of line q: m = [(8 − 4)/(1 − ( − 1))] = [4/2] = 2.

- Slope of line AB: m
_{1}= [( − 4 − 5)/(4 − 1)] = [( − 9)/3] = − 3 - slope of line CD: m
_{2}= [(2 − 3)/(3 − ( − 2))] = − [1/5]. - m
_{1}*m_{2}= [3/5] − 1

- The slope of line q is :m = [(6 − 2)/(1 − 3)] = − 2
- so the slope of line p is also − 2.
- the slope of line p is: m = [(4 − 9)/(4 − (2 − x))] = − 2
- − 5 = − 2(4 − (2 − x))
- − 5 = − 2(2 + x)
- 2.5 = 2 + x

- the slope of line p is : m = [( − 10 − 4)/(4 − ( − 3))] = [( − 14)/7] = − 2

- The slope of the line is: m = [(7 − 4)/(5 − (x + 3))] = − 3
- [3/(2 − x)] = − 3
- [1/(2 − x)] = − 1
- x − 2 = 1

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Slope of Lines

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Definition of Slope 0:06
- Slope Equation
- Slope of a Line 3:45
- Example: Find the Slope of a Line
- Slope of a Line 8:38
- More Example: Find the Slope of a Line
- Slope Postulates 12:32
- Proving Slope Postulates
- Parallel or Perpendicular Lines 17:23
- Example: Parallel or Perpendicular Lines
- Using Slope Formula 20:02
- Example: Using Slope Formula
- Extra Example 1: Slope of a Line 25:10
- Extra Example 2: Slope of a Line 26:31
- Extra Example 3: Graph the Line 34:11
- Extra Example 4: Using the Slope Formula 38:50

### Geometry Online Course

### Transcription: Slope of Lines

*Hello--welcome back to Educator.com.*0000

*The next lesson is on the slope of lines; this might be a little bit of a review for you from algebra.*0002

*But this whole lesson is going to be on slope.*0010

* Slope is the ratio between the vertical and the horizontal, or we can say "rise over run."*0014

*Rise, we know, is going up and down; and then, the run is going left and right.*0027

*So, when we talk about slope, we are talking about the vertical change and the horizontal change.*0033

*For slope, we use m; so the slope of a line containing two points with coordinates (x _{1},y_{1})*0044

*and (x _{2},y_{2}) is given by this formula right here.*0057

*Now, (x _{1},y_{1}), these numbers right here, and (x_{2},y_{2}), those numbers, are very different from exponents.*0061

*They are not to the power of anything; it is just saying that it is the first x and the first y.*0073

*So, we know that all points are (x,y), and so, this right here is just saying that this is the first x and the first y.*0083

*And this is also x and y, but you are just saying that it is the second point; it is the second x and the second y.*0094

*Because you have two x's and two y's, you are just differentiating the points; this is the first (x,y) point, and this is the second (x,y) point.*0103

*It doesn't matter which one you label as first and which one you label as second.*0112

*You are just talking about two different points.*0116

*And when you have two points, then the slope is going to be (y _{2} - y_{1})/(x_{2} - x_{1}).*0118

*You are going to subtract the y's, and that is going to be your vertical change, because y, you know, is going up and down.*0130

*And x _{2} - x_{1} is your horizontal change, the difference of the x's, which is going horizontally.*0139

*Now, it doesn't matter...like I said, if you are going to subtract this point, this second y, from this y,*0150

*then you have to make sure that you subtract your x's in the same order.*0163

*If you are going to subtract y _{2} - y_{1}, then it has to be x_{2} - x_{1} for the denominator.*0168

*It can't be (y _{2} - y_{1})/(x_{1} - x_{2}).*0174

*If you do y _{2} - y_{1} over here, you cannot do x_{1} - x_{2}.*0179

*You can't switch; it has to be subtracted in the same order, or else you are going to get the wrong answer.*0185

*And this right here is just saying that x _{1} and x_{2}, these numbers, can't equal each other,*0190

*because if they do, then this denominator is going to become 0.*0197

*If x _{1} is 5, and x_{2} is 5, then it is just going to be 5 - 5, and that is going to be 0.*0201

*And when we have a fraction, you can't have 0 in the denominator, or else it is going to be undefined.*0212

*So, that is what it is saying right here: they should not equal each other, or else you are going to have an undefined slope.*0218

*Let's find the slope of these lines: here we have (-4,-2) and (5,3).*0229

*Now, you can do this two ways: you can use the slope formula by doing (y _{2} - y_{1})/(x_{2} - x_{1});*0239

*if you have a coordinate plane, and it is marked out for you--you have grids that show each unit--*0252

*then you can count; you can just go from one point to the other point,*0262

*and you can just count your vertical change and count your horizontal change; you could do it that way.*0269

*But since these are not labeled--each unit is not labeled out--let's just use the slope formula.*0275

*Here, if I make this (x _{1},y_{1}), (x_{2},y_{2}), then my slope is going to be (-2 - 3)...*0285

*so then, this value is (y _{2} - y_{1}, which is 3), over (-4 - 5).*0301

*Now, I could do (3 - -2); I can go that way if I want, but if I do that, if I choose to do this one first,*0312

*(3 - -2), then I have to do (5 - -4); you have to be in the same order.*0321

*If you do 3 minus -2, then you can't go with (-4 - 5); you can't go the other way then.*0327

*It doesn't matter which one you start with; but when you do your x, you have to do it in the same order.*0338

*This one right here is -5/-9, which is just 5/9.*0345

*Now, without solving slope, if you look at the line, you should be able to tell if the slope is going to be positive, negative, 0, or undefined.*0358

*For this one, since the slope measures how slanted a line is, how tilted a line is, if we look at this line,*0374

*imagine a stick man (I like to call him "stick man," because I can only draw stick figures) walking on this line.*0388

*Now, he can only walk from left to right, because let's say you read this--you have to read from left to right.*0398

*So then, it can only go from left to right; he is walking uphill, and that would be a positive slope.*0407

*This is a positive slope; if the stick man is walking uphill, it is a positive slope.*0416

*If the stick man is walking downhill, like the next one (again, he can only walk from left to right)--he is going to walk downhill, so this is a negative slope.*0426

*Without even solving, I know that my slope is going to be negative.*0439

*This is positive; it is positive 5/9.*0443

*Now, the slope for this one--I know, before I even solve it, that it is going to be negative.*0446

*So, after I do solve it, if I get a positive answer, then I know that I did something wrong, because it has to be negative.*0451

*For this one, the slope is 5 - -4; and make sure that you are going to find the difference of the y's for your numerator.*0463

*Don't do your x's first; the numerator is y's; the denominator is x's.*0475

*I went from this to this, so then I have to do -2 - 3.*0482

*So then, this is...minus a negative is the same thing as a plus, so 5 + 4 is 9, and then -2 - 3 is -5.*0489

*So, this is -9/5; and I have a negative slope, so that is my answer.*0502

*A couple more: here I have a horizontal line; my slope is (y _{2} - y_{1})...(-3 - -3), over (-6 - 4); this is 0,*0519

*because -3 + 3 is 0; this is -10; well, 0 over anything is always 0; so the slope here is 0.*0541

*Now, let's bring back the stick man: if stick man is walking on this, he is not walking uphill or downhill; he is just walking on a flat surface.*0554

*If he is walking on a flat surface, since slope measures how slanted a line is, it is not slanted at all--it is just flat; that is why the slope is 0.*0563

*Whenever it is flat, it is a horizontal line, and the slope will be 0--always.*0573

*It doesn't matter if it is up here or down here; as long as it is a horizontal line, your slope is going to be 0.*0580

*The next one: 4 - -4...be careful with the negatives: it is 4 minus -4; -2 - -2; change those to a plus--*0592

*minus a negative is also a plus--so 4 + 4 is 8, over -2 + 2...is 0.*0615

*Now, look at the difference between this one and this one.*0624

*In this one, the 0 is in the numerator; if it is in the numerator, it makes it just 0; 0 is a number, just like 5, 6, -3;*0628

*those are all numbers, and 0 is a number; so your answer for this problem, your slope, is 0; you have a slope; it is 0.*0640

*And in this problem, we cannot have 0 in the denominator--it is just not possible.*0650

*So, since you did come up with a 0 in the denominator, this is going to be undefined.*0657

*You can also say "no slope"; in this case, you do have a slope--the slope is 0; in this case, you do not have a slope.*0669

*There is no slope; it doesn't exist; it is undefined, because the denominator is 0.*0680

*So, my answer is just "undefined."*0685

*And then, to bring back the stick man: since it is a man, it can't do this--this is like walking up a wall.*0689

*Stick man can't walk up a wall; it is not possible--it can't do it.*0702

*He can't walk up a wall; he is not Spiderman; he can't walk up a wall.*0706

*So, in this case, this man can't do this; if he can't walk up this wall, it is undefined; it can't be done; there is no slope.*0711

*If he is walking on a horizontal--no slant at all--it is 0.*0724

*If he has to walk up a wall (which is impossible), then it is an undefined slope.*0731

*If the stick man is walking uphill, it is a positive slope; downhill is a negative slope; a horizontal line is 0; a vertical line, like a wall, is undefined.*0737

*You can't walk up a wall.*0749

*A couple of postulates: If we have two non-vertical lines that have the same slope, then those lines are parallel,*0754

*because again, slope measures how slanted a line is.*0769

*So, if I have two lines that are slanted exactly the same way, then they are going to be parallel.*0775

*Again, two lines that have the same slope are parallel.*0788

*And this part right here: "if and only if"--now, we went over conditionals, if/then statements;*0794

*to change this one right here (let's go over this...number 1)...two non-vertical lines have the same slope if and only if they are parallel.*0807

*This just means that this conditional and its converse are both true.*0819

*It is basically two statements, two conditionals in one.*0833

*I can say, "If two lines have the same slope, then they are parallel."*0840

*And this would be the converse: I can say, "If two lines are parallel, then they have the same slope."*0865

*The statement and its converse are both true: this is true, and this is true.*0893

*So, just instead of writing each of those conditionals separately, you can write them together by "if and only if."*0897

*It just means that this statement and its converse (converse means, remember, that you switch the hypothesis and the conclusion) are both true.*0908

*So then, you can just use "if and only if."*0919

*If two lines have the same slope, then the two lines are parallel.*0925

*Or you can say, "If two lines are parallel, then they have the same slope."*0930

*Either way, parallel means same slope; same slope means parallel.*0934

*Now, the next postulate is talking about perpendicular lines: Two non-vertical lines are perpendicular if and only if the product of their slopes is -1.*0939

*Now, "the product of their slopes is -1"--that means that, if, first of all, I have a line like this,*0957

*and I have a line like this, let's say they are perpendicular; and the slope of this line, let's say, is 1/2*0970

*(it has to be positive; it is going uphill); then the slope of this line is going to be the negative reciprocal,*0979

*meaning that you are going to make it negative; if it is negative already, then you are going to make it positive;*0990

*so, the slope of this line will be negative...and then the reciprocal of it will be 2/1.*0997

*So then, it is saying that the product of their slopes is going to be -1; so 1/2 times -2 is -1.*1006

*Just think of it as: If you have two perpendicular lines, then the slopes are going to be negative reciprocals of each other.*1023

*And if you multiply those two slopes, then you should get -1, always.*1032

*OK, parallel or perpendicular lines: you are given points A, B, C, and D; you want to determine if line AB is parallel or perpendicular to CD.*1040

*So, to determine if the two lines are parallel or perpendicular, then you have to compare their slopes.*1058

*So, for line AB, I need to use points A and B.*1066

*If I find the slope using these two points, the slope of AB is going to be -6 - 0, y _{2} - y_{1}, over x_{2} - x_{1}.*1070

*And that is -6/-3, so we have 2.*1093

*And then, the slope of CD is y _{2}, -3, minus -4, over 4 - 2; this is 1/2, so this is positive 1 over 2.*1100

*Did I get that right?--yes.*1133

*In this case, it is going to be neither, because here we have AB; (-6 - 0)/(-2 - 1) becomes positive 2.*1138

*And then here, this is -3 - -4, and 4 - 2; for this, I get positive 1/2.*1157

*Now, it looks like they are going to be perpendicular, but remember: they have to be the negative reciprocal of each other.*1168

*If this is 2, this is 2/1, and the inverse, or the reciprocal, is 1/2; but they are not negative--it is not negated.*1176

*So, if I multiply 2/1 times 1/2, I am only going to get 1, not -1; so this is neither.*1188

*OK, find the value of x if the line that passes through this point and this point is perpendicular to the line that passes through (-1,6) and (-2,8).*1204

*We are given our two points that we have to find the slope of.*1220

*But from those two points, one of the values, the x-value, is missing.*1227

*That means that we need the slope.*1235

*They didn't just give us the slope in this problem; they didn't just hand it to us.*1239

*We have to actually solve for the slope, because we know that it is perpendicular to a line that passes through these two points.*1243

*So, basically, the points that I have to use are (x,4) and (-3,3).*1255

*I have to find x; and this is another line, and I am just going to use that line to find the slope,*1266

*because I have my slope that I need that has a relationship with the slope of this line.*1278

*So, to find the slope of this line right here that passes through these points,*1285

*I am going to do (6 - 8), (y _{2} - y_{1}), over (-1 - -2); this is -2/1, so the slope is -2.*1293

*But since I know that my line is perpendicular to this line, my slope is going to be the negative reciprocal of this slope.*1307

*If this slope is -2, then my slope is going to be positive 1/2, positive one-half.*1322

*That is what I need to use: the slope is positive 1/2.*1333

*Now, using the slope formula, I know that this is (y _{2} - y_{1})/(x_{2} - x_{1}).*1338

*Well, I can just fill everything in, except for this, and then use that as x _{1}.*1350

*1/2 is my m; y _{2}...if this is (x_{1},y_{1}), (x_{2},y_{2}),*1356

*y _{2} is 3, minus 4, over -3, minus x; since I don't know this value, which is what I am solving for, I can just leave it like that.*1365

*And then, from here, I have to solve this out.*1384

*I can solve this out a couple of ways: first of all, since this is a fraction equaling a fraction, I can use proportions.*1388

*I can make (-3 - x) times 1 equal to 2 times 3 minus 4; or let me just do this--let me just simplify this first.*1399

*1/2 = -1/(-3 - x); or I can just multiply...*1411

*I have a variable; the variable that I am solving for is x, and that is in the denominator.*1423

*If I want to solve for the variable, it cannot be in the denominator, so I have to move it out of the denominator.*1427

*I can do that by multiplying both sides or the whole thing by -3 - x;*1433

*or again, since this is like a fraction equaling a fraction, like a proportion, I can just do that.*1439

*So, just make -3 - x equal to...and then, I am just multiplying it this way...equaling this; it is -3 - x = -2;*1444

*if I add 3, then I get -x = 1; x = -1.*1459

*So again, you are going to find your slope.*1469

*They might not just hand you the slope; they might not tell you what the slope is directly.*1476

*So then, you have to find it this way; they will give you another line that has a relationship with your line, your slope.*1483

*So, you have to find the slope of that other line, and then use that slope to find your slope.*1496

*And then, plug it all into the slope formula; and then from there, you just solve.*1503

*Let's do a few examples: Find the slope of the line passing through the points.*1510

*Again, here is the slope formula; this equals...it doesn't matter which one I use first, so I will just use (-2 - 5) first.*1517

*That means that I have to use this one first; so it is (3 - -4).*1536

*This becomes -7/7, which is equal to -1; and then, for this one, the slope is (0 - 6)/(-7 - -7).*1542

*This is going to be -6/0; 0 is in the denominator, which means that I have an undefined slope.*1564

*And that just means that the line that is passing through these points is going to be a vertical line; vertical lines have undefined slopes.*1580

*Find the slope of each line: now, they don't give you the points--they just show me the lines.*1593

*And I have to see what points the lines are going through to find the slope.*1602

*Let's see, let's look for the slope of n first; here is n.*1612

*Now, remember: for slope, I can do this two ways: I can find two points on this line, like this and like this--*1618

*those are two points on the line (or here is another point; it doesn't matter--any two points on the line);*1630

*you can find the coordinates of the points and use the slope formula.*1636

*For two points, find the coordinates and use the slope formula.*1642

*Or an easier way, in this problem: Since we have all of these grids marked out for us, I can just*1646

*(because slope is rise over run, the vertical change over the horizontal change; rise is how many it is going up or down,*1656

*and then run is how many is going left or right)--whenever I go up (here, this is the positive y-axis), any time I am counting upwards,*1668

*it is a positive number; if I am counting downwards, then it is a negative, because I am going smaller.*1683

*If you are going up, it is a positive number; if you are going down, if you are counting down, then it is a negative number.*1690

*The same thing for x: if you are moving to the right, it is a positive number; if you are moving to the left, it is a negative number,*1696

*because it is getting larger as you go to the right; and as you go to the left, you are moving towards the negative numbers.*1703

*You are getting smaller, so it is negative if you are going to the left.*1709

*To find the slope of n, I am just going to do rise over run; I am going to just count my vertical and horizontal change.*1715

*You go from any point to any other point on the line.*1724

*I can start from here; I am going to go one up, because it is on this right here.*1729

*My vertical change: I only went up one; remember, up is positive, so to find the slope of n, it is positive 1*1740

*(that is my rise), and then I am going 1, 2 to the right--that is positive 2, so the slope is 1/2.*1754

*Now, remember: I can also go from any point to any other point on the line.*1767

*So, if I start from this point, let's say I am going to go from this point, and then (I didn't see this point, so) to this point;*1773

*then I can go down 2 (remember: down 2 is negative 2), over...then I am going to go 1, 2, 3, 4.*1781

*And that is to the left, so that is negative 4; -2/-4 is the same thing as 1/2.*1797

*It doesn't matter how you go from whichever point to any other point on the line, as long as both points are on the line,*1808

*and as long as you make it a positive number going up, a negative number going down, positive to go right, and negative to go left.*1817

*You are going to get the same answer; you are going to get the same slope.*1826

*The slope of n is 1/2; then the slope of p (let me use red for this one): let's see, I have a point here, and I have another point here.*1830

*So again, I can go from this point to that point, or I can go from that point to that point; it doesn't matter.*1853

*Let's start right here: I am going to go 1, 2, 3; I went up 3, so that is a positive 3.*1858

*And then, from here, I go to the left 1, which is a negative 1.*1869

*3/-1 is the same thing as -3, so my slope of p is -3.*1876

*Or I could go from this point to this point; that would be to the right one (that is positive 1), over down 3 (1, 2, 3);*1883

*oh, I'm sorry; I did horizontal over vertical, which is wrong; so I have to go this way--vertical first.*1893

*1, 2, 3: that is a -3, and to the right 1--that is positive 1; so this is also -3, the same thing.*1902

*The next line is line q (I will use red for this one, too): this is a vertical line.*1916

*Automatically, I know that that has an undefined slope. I can also just...*1932

*Now, I know that this line is not really completely lined up with the grid, but sometimes when you transfer*1939

*this into this program, or move things into this program, it might shift a little bit.*1947

*But think of this line as being on 2 right here, as x being 2.*1951

*Let's say I have this point right here, and then any other point--that point right there.*1960

*All that I am doing is: my vertical change is going down to -2; my horizontal is nothing: 0.*1964

*I am not moving to the right or left at all; that is 0.*1975

*So, we have a 0 in the denominator; this is an undefined slope.*1979

*And again, I knew that because this is a vertical line; the stick man can't walk up that line; so it is an undefined slope.*1989

*And the last one, for line l: any two points...*1999

*Again, this line is shifted a little bit, but I can just do that if I want.*2007

*Vertical change first: the vertical change is 0, because I am not moving vertically; to get from this point to this point, I don't go up or down at all.*2014

*So, it is 0 over...and then, I can move 1, 2, 3 to the right; so no matter what the bottom number is, my slope will be 0.*2021

*The slope of the l is 0; again, it is a horizontal line, so it is not slanted; it is not going uphill or downhill--nothing.*2035

*It is just horizontal; then the slope is 0.*2044

*The next example: Graph the line that satisfies each description; slope is 2/3 and passes through (-1,0).*2052

*You just have to graph this first one; let's say I am going to graph it right up here.*2066

*Now, just a sketch will do; let's say...here is my x; here is my y; (-1,0) is right there.*2075

*My slope is 2/3; so again, this is rise over run.*2103

*Now, I can use the same concept, the positive going up and negative going down, positive to the right and negative to the left.*2110

*The top number, the rise, to go up and down: I have a positive 2--that means I am going to go up 2, because it is positive.*2120

*From here, I am going to go 1, 2; and then, I have 3 that I am going to move to the left or to the right;*2130

*but since it is a positive 3, I am going to move to the right: 1, 2, 3.*2139

*Now, from this point, I can go down if I want to, because 2/3, that slope, is the same thing as -2/-3.*2150

*So, if I go -2, I am going to go down 2: 1, 2; and then, -3 is to the left, so 1, 2, 3; there is my line, right there.*2163

*This is the second one: it passes through point (3,1) and is parallel to AB with A at this point and B at that point.*2182

*Again, they don't give us our slope; they just give us the point that we need to use.*2194

*Our line is going through this point, and we don't have the slope of our line;*2201

*instead, they give us the slope of another line, line AB; and they say that it is parallel to it.*2205

*So, as long as we find the slope of AB, since it is parallel, we know that our slope will just be the same as this slope.*2211

*The slope of AB is (4 - 3)/(-1 - -2), which is 1 over...this is 1...so 1.*2222

*Now, since our slope is parallel, again, our slope is 1.*2238

*And then, this is our point; so we have point (3,1), and the slope is 1.*2247

*To graph (x,y), (3,1), it is 1, 2, 3; and 1; there is our point that our line is passing through.*2258

*And then, our slope is 1; 1 is the same thing as 1/1, so positive 1 is up 1, to the right 1; also, positive 1 is up 1.*2291

*And then again, you can just do -1/-1; that is the same thing as 1.*2308

*So, from here, I can go down 1, left 1; down 1 is -1; left 1 is -1.*2313

*And that is going to be a line like that.*2322

*The last example: Determine the value of x so that a line through the points has the given slope.*2331

*Again, they give us a slope, and then we have to find the missing value, which is x.*2338

*Since we know that the slope formula is (y _{2} - y_{1})/(x_{2} - x_{1}),*2345

*if I make this (this is (x,y), and this is also (x,y)) my first point, and this is my second point--*2354

*so that is (x _{2},y_{2})--then my slope is y_{2}, which is -5, minus 1, over x_{2}, -3, minus x.*2366

*Now, again, you can turn this into a proportion; or I can just multiply this out to both sides.*2385

*I can multiply this to this right here to cancel it out, and then multiply to the other side and distribute that; I could solve it that way.*2397

*Or I could just make this a proportion: 2/1 = -6/(-3 - x); so to continue right here, it is going to be 2(-3 - x) = -6.*2406

*This is -6 - 2x, and you just distribute that; that equals -6; -2x = 0; x = 0.*2430

*So, we have 0 as our x for this problem.*2444

*OK, the next one: again, plugging everything into the slope formula, we have 4/3 = (-2 - -6)/(x - 7).*2450

*So, 4/3 =...this is -2 + 6, so this is 4, over x - 7.*2472

*OK, well, in this problem, again, you can multiply x - 7 to both sides to get it out of the denominator,*2482

*because since you are solving for x, it cannot be in the denominator.*2492

*Or you can cross-multiply using proportions, because it is a fraction equaling a fraction.*2497

*Or, since this 4 numerator equals this 4 numerator, then the denominator has to equal the denominator, so you can make 3 equal to x - 7.*2505

*So, let's just solve it out, multiplying: I can multiply this side by (x - 7) like that,*2518

*and multiply this side by (x - 7); then, it is going to be 4/3x minus 28/3 equaling 4.*2529

*Now, this is actually probably the harder way to do it; but I just wanted to show you how to multiply it to both sides.*2553

*This is a binomial that, again, you are just multiplying to both sides.*2561

*But the easiest way would be to make (x - 7) equal to 3: because 4 = 4 (the top), then 3 = x - 7 there.*2567

*So, let's just continue out this way: if I add 28/3 to both sides, this is going to be the same thing as 12/3 + 28/3,*2577

*and that is just because I need a common denominator; that is equal to 4/3x.*2593

*That equals...this is 40/3...if I multiply the 3's to both sides, this will be 4x = 40; x = 10.*2605

*So here, x = 10, this value right here.*2626

*And if we solved it the other way, 3 = x - 7, then you would just add 7, so x would be 10.*2632

*That is it for this lesson; thank you for watching Educator.com.*2642

0 answers

Post by Jeremy Cohen on August 27, 2014

where is the -6 coming from

3 answers

Last reply by: Jing Chen

Sat Aug 26, 2017 11:25 AM

Post by jeeyeon lim on December 31, 2012

How do I know which coordinate is x1 , y1 and x2, y2k? Do I just choose on randomly?