1. CHAPTER 8 Intercepts and Slope-Intercept Form

2. Objectives The student will be able to:
find the x- and y-intercepts of linear equations
Write Standard for of Linear equation to Slope-Intercept equation (function form)

3. What does it mean to INTERCEPT a pass in football?
The path of the defender crosses the path of the thrown football.
In algebra, what are x- and y-intercepts?

4. What are the x- and y-intercepts?
The x-intercept is where the graph crosses the x-axis.
The y-coordinate is always 0.
The y-intercept is where the graph crosses the y-axis.
The x-coordinate is always 0.
(2, 0)
(0, 6)

5. Find the x- and y-intercepts. 1. x - 2y = 12
x-intercept: Plug in 0 for y.
x - 2(0) = 12
x = 12; (12, 0)
y-intercept: Plug in 0 for x.
0 - 2y = 12
y = -6; (0, -6)

6. Find the x- and y-intercepts. 2. -3x + 5y = 9
x-intercept: Plug in 0 for y.
-3x - 5(0) = 9
-3x = 9
x = -3; (-3, 0)
y-intercept: Plug in 0 for x.
-3(0) + 5y = 9
5y = 9
y = ; (0, )

7. Find the x- and y-intercepts. 3. y = 7 ***Special case***
x-intercept: Plug in 0 for y.
Does 0 = 7?
No! There is no x-intercept. None
What type of lines have no x-intercept?
Horizontal!
Remember VUXHOY?
Horizontal lines…y = 7…y-int = (0, 7)

8. What is the x-intercept of 3x – 4y = 24?
(3, 0)
(8, 0)
(0, -4)
(0, -6) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

9. What is the y-intercept of -x + 2y = 8?
(-1, 0)
(-8, 0)
(0, 2)
(0, 4) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

10. What is the y-intercept of x = 3?
(3, 0)
(-3, 0)
(0, 3)
None 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

11. Next Lesson:
Converting Standard Form Linear Equation to Slope-Intercept Form Linear Equation

12. Important!!!
This is a big concept in Algebra 1. You need to thoroughly understand this!
Slope – Intercept Form
y = mx + b
m represents the slope
b represents the y-intercept

13. Writing Equations
When asked to write an equation, you need to know two things – slope (m) and y-intercept (b).

14. Example 1: Writing Equations
Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6.
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
We have both!! Plug them into slope-intercept form
y = mx + b
y = 2x + 6 2 6

15. Writing Equations
Write an equation in slope-intercept form for the following:

16. y = -3x – 4 y = -4x – 3 y = -3x + 4 y = -4x + 3
Write the equation of a line that has a y-intercept of -3 and a slope of -4.
y = -3x – 4
y = -4x – 3
y = -3x + 4
y = -4x + 3

17. To find the slope and y-intercept of an equation, write the equation in slope-intercept form: y = mx + b.
Find the slope and y-intercept.
y = 3x – 7
y = mx + b
m = 3, b = -7

18. Find the slope and y-intercept.
2) y = x
y = mx + b
y = x + 0
3) y = 5
y = 0x + 5
m =
b = 0
m = 0
b = 5

19. Find the slope and y-intercept. 5x - 3y = 6
m =
b = -2

20. Find the slope and y-intercept. 2x + 2y = 4
Write it in slope-intercept form.
(y = mx + b)
2x + 2y = 4
- 2x x
2y = -2x+4
y = -x + 2
m = -1
b = 2

21. Find the slope and y-intercept. x + 2y = 6
Write it in slope-intercept form.
(y = mx + b)
x + 2y = 6
- x - x
2y = -x + 6
y = - 1 x + 3 2
m = - 1 2
b = 3

22. Find the slope and y-intercept. 8x + 2y = -4
Write it in slope-intercept form.
(y = mx + b)
8x + 2y = -4
-8x x
2y = -8x - 4
y = - 4x - 2
m = -4
b = -2

23. Find the slope and y-intercept of y = -2x + 4
m = 2; b = 4
m = 4; b = 2
m = -2; b = 4
m = 4; b = -2