WEBVTT mathematics/basic-math/pyo
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Welcome back to Educator.com.
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For the next lesson, we are going to go over the coordinate plane.
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This right here is called the coordinate plane; it consists of two lines like this.
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This right here, the horizontal line, is called the x-axis.
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The vertical line is the y-axis; together they make up the coordinate plane.
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Think of the coordinate plane as like a map.
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It is a map; we are going to place points along this map.
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We have to label each point based on the x-axis and the y-axis.
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That is the coordinate plane.
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These axes, the x-axis and the y-axis, break the coordinate plane into four sections.
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One, two, three, four, those four sections are called quadrants.
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The first quadrant is this space right here; this is called quadrant one.
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Going over to this side, this is quadrant two; then down, this is quadrant three.
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The last one is quadrant four; those are the four sections of the coordinate plane.
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Each axis is numbered; it is labelled.
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Here, this point right here is going to start off at 0.
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It is going to go 1, 2, 3, 4, 5, and so on; 1, 2, 3, 4, 5.
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Again this is 0; this way, then it is going to go negative.
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See how it goes positive this way.
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If you go the other way, it is going to go negative; -1, -2, -3, -4, -5, and so on.
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Same thing for the y-axis.
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If you go upwards, it is going to go positive.
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It is going to go 1, 2, 3, 4, 5.
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The arrows represent continuation; it is going to keep going on forever.
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It doesn't just stop at 5; it is going to keep going.
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Down this way, it is going to be negative; -1, -2, -3, -4, -5.
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Next right here, a number on the x-axis paired with the number on the y-axis is going to give us an ordered pair.
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You are going to look for the number on the x and the number on the y.
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Together it is going to map out your location on the coordinate plane.
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That point is called an ordered pair; it is going to be written like this.
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In parentheses, you are going to have two numbers.
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The first number is going to be your x number; that is called the x-coordinate.
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The second number is going to be your y coordinate.
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It is always going to be x and then y.
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X always has to come first; (x, y) for short.
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(x, y), that is going to be your ordered pair.
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That is going to map out your location on the coordinate plane.
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This point where the x-axis and y-axis meet, that is called the origin.
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That is right there.
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If you look at the x-number, the x-number, it is 0.
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The x-number is 0; the y-number is also 0.
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The origin is (0, 0); that is the ordered pair for the origin.
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If I put a point right here on the coordinate plane, that ordered pair, what is the x-number?
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If you look, this point is paired with an x-number and a y-number.
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This point is going to have a x-number of 3 and a y-number of 1.
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The ordered pair for this point is (3, 1).
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Be careful that you don't mix those up, switch them up.
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It is not (1, 3); that is not the same thing.
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(1, 3), if I say (1, 3), because I said 1 first, that means I am talking about 1 on the x-axis.
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(1, 3) would be 1 on the x; 3 on the y.
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Where do they meet?--right there, that would be (1, 3).
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(1, 3) and (3, 1) are not the same thing; be careful with that.
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Always make sure the first number is your x-coordinate on the x-axis, the horizontal line.
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The second number is your y-axis, the number on your vertical line.
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That is the coordinate plane.
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Again we have the x-axis, the y-axis; each of the four sections are called quadrants.
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It starts off with this right here, quadrant one, quadrant two, quadrant, three, and quadrant four.
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Remember when you are writing out the numbers, this number is always 0.
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It is going to go positive to the right and negative to the left.
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On the y-axis, positive when you go up, negative when you go down.
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Everything together, the coordinate plane which is like the map, the ordered pairs, the quadrants,
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all of this that have to do with these points, the plane, all that is called the coordinate system.
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It is like a system of all these things together.
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Again a coordinate plane, each of these are just marked for you.
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We have three points, A, B, and C.
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Here is A; here is B; here is C; we want to write the coordinates.
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In other words, we want to know the ordered pairs.
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Find the ordered pairs of A, B, and C.
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We know that this is the x and that is the y.
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Let's start with A, this point right here.
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What is the x-number that makes up this point?--1.
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What is the y-number?--1.
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For A, my x-number, the number on my x-axis, is 1.
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The number on the y-axis is 1.
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The ordered pair or the coordinates for A is (1, 1).
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I am just going to write... because this is the name of the point.
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A is what that point is labelled.
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You can just write it in front of that ordered pair.
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Next is B; again I am looking for the x-number first.
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The x-number, the number on this x-axis that makes up this B is -1.
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The y-number, -2.
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They are negative numbers; but it is fine.
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You are just listing them out like that, same way as when you have positive numbers, (-1, -2).
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The next one is C; the x-number for C is 2.
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The y-number for C is -1.
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Those are the coordinate for A, B, and C.
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Let's do our examples now; graph each point on the coordinate plane.
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The first one, A is (4, 2).
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Remember this is the x-number; this is the y-number.
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I am going to label this as x; this as y.
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4, you are going to look for 4 on the x-axis.
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4; this is -4; here is 4.
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Then look for 2 on the y-axis; here is 2.
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Where do they meet?--right there.
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This is A; I can label that point as A.
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Next, B is (-3, 0); the x is -3; the y is 0.
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-3 on the x is right here; 0 on the y.
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Where is 0?--0 is right there.
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(-3, 0), that means I am not moving any up or any down because there is no y.
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If the y was 1, I would have to move up 1.
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If y was -1, I would have to move down 1.
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But y is 0 so I stay here; that is my B.
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Next, x, y; 2 is x; y is 1.
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Where do they meet?--right there; that is C.
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Next is (-4, -2).
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-4 on the x is right there; -2 on the y is right there.
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Right there, they intersect at that point right there; that point is called D.
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That is it for this example.
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The next one, write the coordinates and quadrant for each point.
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It is like the same thing that we just did a couple examples ago.
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First let's start with A; remember this is my x, this is my y.
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Look for the x that makes up this point right here.
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A is -1; that is my x; y is a -3.
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We also have to state what quadrant it is in.
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Remember that this right here, this section, any points that fall in this section right here is quadrant one.
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This section is quadrant two; quadrant three; and quadrant four.
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If a point is on let's say right here, that doesn't fall under any quadrants.
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That wouldn't be considered quadrant one or quadrant four.
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In that case, you are just going to say that it is on the x-axis.
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Or in this case, if a point lands right here.
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Then it is not in quadrant three or four; it is actually on the y-axis.
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This quadrant, point A is in quadrant three; let's just say quadrant three.
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B, point B is... x is 1, y is 2; (1, 2); that is in quadrant one.
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C is right there; 3 as my x; -1 as my y.
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That is in quadrant four.
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D, x is -3; y is 3; that is quadrant two.
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Example three, name two points from each of the four quadrants.
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It is a little bit hard to do when you don't have the coordinate plane.
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Let's draw out a coordinate plane.
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We don't have to draw it too big because we are not going to be plotting any points.
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Here is the x; here is the y.
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I know this is quadrant one; quadrant two; quadrant three; and quadrant four.
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The trick here is to figure out whether my x-coordinates are going to be positive or negative
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and my y-coordinates are going to be positive or negative.
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Quadrant one, if you look here, all the points that have this as my x and this as my y,
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any points that pair up with this part of my x, that part of my y, is going to be in quadrant one.
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I know that here as I get to these numbers, it is going to be positive.
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This is +1, +2, +3, so on.
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My x-coordinate is going to be positive; it is a positive number; positive.
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My y-coordinate is also going to be positive because these are positive numbers here; positive, positive.
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Any ordered pair that has a positive number paired with a positive y-number is going to be in quadrant one.
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For quadrant one, I have to name two points.
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Any ordered pair with a positive x, positive y, is in quadrant one.
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(1, 2), that is in quadrant one; what else?
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(3, 4), that is also in quadrant one.
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Look at quadrant two; quadrant two, all points with this part of my x.
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Those are my negative numbers.
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A negative x with this part of my y is going to be in quadrant two.
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Then when I list my points in quadrant two,
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it is going to be a negative x number with a positive y number.
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Does that make sense?--it is negative.
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All these numbers are negative here.
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This is -1, -2, -3; it has to be a negative x-coordinate.
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Then paired with a positive y coordinate is going to be in quadrant two.
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(-1, +2) is right there; it is in quadrant two.
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Again negative x, positive y; (-3, 4).
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Quadrant three, again any numbers or any ordered pairs paired with a ?x with this part of the y-axis.
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That is negative also; negative and a negative is going to be in quadrant three.
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This is going to be a negative x, negative y.
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(-1, -2) here is -1; here is -2.
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Another one, (-3, -4).
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For quadrant four, again positive x; how about the y?
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It is going to be any ordered pairs paired with this side and this side.
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Positive x, negative y; positive x, 1; negative y, -2.
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Positive x, 3; negative y, -4.
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Those two points are going to fall under quadrant four.
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The fourth example, we are just going to graph more points on this coordinate plane.
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I didn't number them; go ahead and number them right now.
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1, 2, 3, 4, let's go up to 5; -1, -2, -3, -4, -5; 1, 2, 3, 4, 5.
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The first point, A; I know this is going to be my x-number; this my y-number.
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0 on my x-number is right here; on this right here, 0.
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3 on my y-number is right here.
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That means my y is going to be 3 and my x is going to be 0.
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Meaning I am not going to have -1.
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I am not going to have 1 as my x; I am going to have 0.
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It is going to be that point right there; this is A.
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The next one is (-2, -1); -2 on my x; -1 on my y.
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They meet right there; here is B.
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C is going to be -5 and then 0 as my y.
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Remember if my y is 1, I go up 1.
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If my y is -1, I go down 1; right there.
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But it is 0; my y is 0; that means I don't move up or down.
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I stay put; that is my C.
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My last point D is going to be 4 and -6.
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-6 on my y-axis is right here; they meet right there.
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That point is labelled D.
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That is it for this lesson; thank you for watching Educator.com.