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### Slope Intercept Form of an Equation

- The
*slope-intercept form*of a linear equation is y = mx + b, where m is the slope and b is the y-intercept of the graph. - Given a graph, you can determine the slope and the y-intercept and then write the equation in slope-intercept form.
- If you are given the equation in slope-intercept form, you can use the information given by the equation to draw the graph without the need to create a table of values.
- In most problems involving linear equations and their graphs, you will be asked to find the equation in slope-intercept form.
- If you are given the slope of a line and a point that is not the y-intercept, first find the y-intercept by substituting the coordinates of the point and the given slope into the slope-intercept form and solving for b. Then you have the information necessary to write the equation in slope-intercept form.
- If you are given 2 points that lie on a line, first use their coordinates to find the slope. The follow the procedure just given to find the y-intercept; you can use either point to do this. Then write the equation in slope-intercept form.

### Slope Intercept Form of an Equation

A line passes through the points (5,4) and (0,8). Find the equation of the line in slope intercept form.

- y = mx + b

slope = [(y_{2}− y_{1})/(x_{2}− x_{1})] - slope = [(8 − 4)/(0 − 5)] = [4/( − 5)]

y = − [4/5]x + 8

A line passes through the points ( - 3,6) and (0, - 6). Find the equation of the line in slope intercept form.

- y = mx + b

slope = [(y_{2}− y_{1})/(x_{2}− x_{1})] - slope = [( − 6 − 6)/(0 − ( − 3))]
- slope = [( − 12)/3]
- slope = − 4

y = − 4x − 6

A line has slope - 4 and passes through ( - 10, - 8). Find its equation in slope intercept form.

- y = mx + b
- m = − 4

b = ? - − 8 = − 4( − 10) + b
- − 8 = 40 + b
- b = − 48

y = − 4x − 48

A line has slope - 1 and passes through (7,15). Find its equation in slope intercept form.

- y = mx + b
- m = − 1

b = ? - 15 = − 1(7) + b
- 15 = − 7 + b
- 22 = b
- y = − 1x + 22

y = − x + 22

A line passes through the points (4,1) and (0,6). Find the equation of the line in slope intercept form.

- slope = m = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - m = [(6 − 1)/(0 − 4)]
- m = [5/( − 4)]
- y = mx + b

y = − [5/4]x + 6

A line has slope - 7 and passes through ( - 8,11). Find its equation in slope intercept form.

- y = mx + b
- m = − 7

b = ? - 11 = − 7( − 8) + b
- 11 = 56 + b
- − 45 = b

y = − 7x − 45

A line passes through the points ( - 2, - 3) and (4, - 2). Find the equation of this line in slope intercept form.

- m = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - m = [( − 2 − ( − 3))/(4 − ( − 2))]
- m = [1/6]
- y = mx + b
- − 3 = [1/6]( − 2) + b
- − 3 = − [2/6] + b
- − 2[4/6] = b

y = [1/6]x − 2[4/6]

A line passes through the points (5, - 4) and ( - 1,6). Find the equation of this line in slope intercept form.

- m = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - m = [(6 − ( − 4))/( − 1 − 5)]
- m = − [10/6] = − [5/3]
- 6 = − [5/3]( − 1) + b
- 6 = 1[2/3] + b

4[1/3] = b

Graph y = 3x − 5

- Identify slope
- m = 3
- Identify intercept
- b = − 5

Graph utilizing slope and intercept

Graph y = [x/2] + 3

- Identify slope
- m = [1/2]
- Identify intercept
- b = 3

Graph utilizing slope and intercept

*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 Intercept Form of an Equation

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
- Slope Intercept Form 0:12
- m (Slope) and b (Y Intercept)
- Example
- Example 1: Slope Intercept Form Equation 2:39
- Example 2: Graph the Equation 5:11
- Example 3: Slope Intercept Form Equation 6:51
- Example 4: Slope Intercept Form Equation 8:50

1 answer

Last reply by: Dr Carleen Eaton

Mon Apr 4, 2016 11:00 PM

Post by Kenosha Fox on April 4, 2016

Dr.Caleen Eaton in example 4 how did you subtract 1/4 from -7?

1 answer

Last reply by: Jessie Carrillo

Sat Jan 2, 2016 3:09 PM

Post by Jessie Carrillo on January 2, 2016

Isnt the answer for example IV y= 1/4 - 7 1/4?

1 answer

Last reply by: Dr Carleen Eaton

Sat Sep 14, 2013 2:29 PM

Post by David Duque Henao on August 6, 2013

Dr Eaton, in the second example you did assign the negative sign to the numerator, can I use it in the denominator resulting in 1/-4 and graph to the left? Is that ok?

0 answers

Post by Victor Castillo on January 26, 2013

OK I figured out the (0,b).....

1 answer

Last reply by: Dr Carleen Eaton

Sun Jan 27, 2013 12:54 PM

Post by Victor Castillo on January 25, 2013

This is very confusing.At 6:43 you said your second point was at (1,4)but you are at (0,4).

0 answers

Post by Victor Castillo on January 25, 2013

Where did (0,b) Come from?