1. The Slope-Intercept Form of a Line
Topic 4.4.3

2. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
California Standard:
8.0 Students understand the concepts of parallel lines and perpendicular lines and how their slopes are related.
Students are able to find the equation of a line perpendicular to a given line that passes through a given point.
What it means for you:
You’ll plot graphs and solve equations using a method called the slope-intercept form of an equation.
Key Words:
slope-intercept form
intercept

3. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Now that you’ve practiced calculating the slope and intercept of a line, you can use the two things together to make plotting graphs easier. –6 –4 –2 2 4 6 y x

4. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
The Slope-Intercept Form of a Line: y = mx + b
In the slope-intercept form the y is alone on one side of the equation.
The slope-intercept form of the equation is:
y = mx + b
Here are a few examples of equations in the slope-intercept form:
y = 3x y = – x y = –x y = x – 4 2 3 1

5. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Guided Practice
In Exercises 1–6, decide whether each equation is in slope-intercept form or not.
1. y = 3x x + 4y = y – 3 = 2(x – 4) 4. y – 8 = 3(x – 4)
5. y = x y = –4x – 1
yes no no no 3 2
yes
yes
Solution follows…

6. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
The Slope-Intercept Form Makes It Easy to Plot Graphs
The slope-intercept form of an equation is really useful for plotting graphs because m is the slope of the line and b is the y-coordinate of the y-intercept.
y = mx + b
y-coordinate of y-intercept
slope

7. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Example 1 1 2 1 2 –6 –4 –2 2 4 6 y x
y = x + 2 1
Plot the graph of y = x + 2.
Solution
y = mx + b = x + 2 1 2
— for a slope of , go up 1 unit for every 2 units across.
Slope = m = 1 2
y-coordinate of the y-intercept = b = 2 — so the y-intercept is (0, 2).
Solution follows…

8. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Example 2 –6 –4 –2 2 4 6 y x
y = –3x – 4
Plot the graph of y = –3x – 4.
Solution
y = mx + b = –3x – 4
Slope = m = –3 — for a slope of –3, go down 3 units for every unit across.
y-coordinate of the y-intercept = b = –4 — so the y-intercept is (0, –4).
Solution follows…

9. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Guided Practice
7. In the equation y = 8x + 5, find the slope.
8. In the equation y = –x + 10, find the slope.
9. In the equation y = 2x + 5, find the y-intercept.
10. In the equation y = 7b – 3, find the y-intercept.
m = 8
m = –1
y-intercept = (0, 5)
y-intercept = (0, –3)
Solution follows…

10. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Guided Practice
In Exercises 11–14, plot each equation on a graph.
11. y = 2x + 3
12. y = x – 6
13. y = –7x – 8
14. y = – x – 4 –6 –4 –2 2 4 6 y x –8 –6 –4 –2 2 4 6 y x 13 12 11 14 1 3
Solution follows…

11. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Guided Practice
In Exercises 15–18, plot each equation on a graph.
15. y = – x + 6
16. y = x – 3
17. y = x
18. y = 6 1 2 –6 –4 –2 2 4 6 y x 17 16 15 18 1 5 3 4
Solution follows…

12. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Solve for y to Get the Slope-Intercept Form
OK, so you know the slope-intercept form of an equation makes drawing graphs a lot easier.
The trouble is, you’ll often be given an equation which isn’t in slope-intercept form.
To get the equation into slope-intercept form, solve for y.

13. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Example 3
A line has the equation Ax + By = C, where B ¹ 0. Solve this equation for y, justifying each step.
Solution
Ax + By = C
Given equation
Ax – Ax + By = –Ax + C
Subtraction property of equality
By = –Ax + C
Division property of equality
Solution continues…
Solution follows…

14. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Example 3
A line has the equation Ax + By = C, where B ¹ 0. Solve this equation for y, justifying each step.
Solution (continued)
The equation is now in slope-intercept form.
The slope, m = –
and the y-coordinate of the y-intercept, b = – . A B C

15. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Example 4
Determine the slope and y-intercept of the line 2x – 3y = 9.
Solution
Step 1: Solve the given equation for y.
2x – 3y = 9
–3y = –2x + 9
y =
y = x – 3 2 3
Now you’ve got the equation in slope-intercept form, y = mx + b.
Solution continues…
Solution follows…

16. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Example 4
Determine the slope and y-intercept of the line 2x – 3y = 9.
Solution (continued)
y = x – 3 2 3
Step 1:
Step 2: Get the slope and y-intercept from the equation.
The slope, m = 2 3
The y-coordinate of the y-intercept, b = –3. So, the y-intercept = (0, –3).

17. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Guided Practice
In Exercises 19-24, find the slope and y-intercept of the line.
19. 3x + 3y = y – 6x = 10
21. 2x – 2y = –7y + 5x = 14
23. –2y + 3x = –5x + 4y = 12
m = –1, (0, 3)
x + y = 3 Þ y = –x + 3
m = 3, (0, 5)
y – 3x = 5 Þ y = 3x + 5
m = 1, (0, – ) 5 2
x – y = Þ y = x –
m = , (0, –2) 5 7
y – x = –2 Þ y = x – 2
m = , (0, –4) 3 2
y – x = –4 Þ y = x – 4
m = , (0, 3) 5 4
– x + y = 3 Þ y = x + 3
Solution follows…

18. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Guided Practice
Write down the equations of the following lines in slope-intercept form.
25. The line with slope 4 that passes through the point (0, 2) The line with slope 2 that passes through the point (0, –6) The line with slope –3 that passes through the point (0, 1).
y = 4x + 2
y = 2x – 6
y = –3x + 1 6 7
28. The line with slope – that passes through the point (0, –3). 6 7
y = – x – 3
Solution follows…

19. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Independent Practice
In Exercises 1–10, find the slope and y-intercept of each equation that’s given.
1. y = x – y = x + 1 1 2 2 3
m = , (0, –5) 1 2
m = , (0, 1) 2 3
3. y = 3x –6y = 3x y = 2(x + 2) y – 4 = 2(x + 1) 7. 7 – y = 5(x + 4) y – 3 = 2(x – 9) 9. 3x + 4y = x + 3y = 9
m = – , (0, –2) 1 2
m = 3, (0, 6)
m = 2, (0, 4)
m = 2, (0, 6)
m = –5, (0, –13)
m = 2, (0, –15) 3 4
m = – , (0, 2)
m = – , (0, 3) 2 3
Solution follows…

20. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Independent Practice
In Exercises 11–15, plot the graph of the given equation.
11. y = x + 5
12. y = – x – y = x + 2
14. y = –x y = 2x 1 3 –6 –4 –2 2 4 6 y x 15 13 11 14 12 1 3
Solution follows…

21. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Independent Practice
In Exercises 16–20, write the equations of the lines in slope-intercept form.
16. A line with slope that passes through the point (0, 4) A line with slope that passes through the point (0, –2). 4 3
y = x + 4 4 3 1 2
y = x – 2 1 2
18. 4x + 2y = x – 3y = 15
20. 3x – 4y = –16
y = –2x + 4
y = 2x – 5
y = x + 4 3 4
Solution follows…

22. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Independent Practice
In Exercises 21–22, write the equations of the lines in slope-intercept form.
21. The line with slope 0 that passes through the point (2, 6) 22. The line with slope 2 that passes through the point (6, 3)
y = 6
y = 2x – 9
Solution follows…

23. The Slope-Intercept Form of a Line
Topic
4.4.3
The Slope-Intercept Form of a Line
Round Up
If m = 0, the slope-intercept form of the equation becomes y = b — the equation of a horizontal line.
If b = 0, the equation becomes y = mx, meaning the line passes through the origin.