Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Slope-Intercept Form A.CED.2

Copyright © by Holt, Rinehart and Winston. All Rights Reserved.

Slope-Intercept Form

A.CED.2


Essential Questions:• How do I write the equation of a line in slope-

intercept form?• How do I graph a line of an equation in the

slope-intercept form?


Glossary Termsslope-intercept form : y = mx + b

x-intercept: where the line crosses the x-axis

y-intercept: where the line crosses the y-axis


What is an intercept?

Y intercept

Y= -4

(0, -4)

X intercept

X = 4

(4,0)


Rules and PropertiesSlope-Intercept Form

y = mx + b

“M” is slope and “b” is y-intercept


Y = mx + b• M is the slope• B is the y-intercept• Leave x and y, simply x and y.• You must have an “x” and “y” !!


Use the slope intercept form to construct a graph of y=2x - 8

• What is the slope and y-intercept?• Slope is 2, and y intercept is (0,-8)• Graph the y intercept and then use the slope

of 2 (convert into 2/1) and rise 2 and run 1 to get your second point.

• Connect the two points and add arrows!


Key SkillsWrite an equation in slope-intercept form for a line.

A line contains the points (–1, 3) and (2, –3).

Find m.

Substitute for x, y, and m in the

equation y = mx + b.

3 = –2(–1) + b

m =–3 – 3

2 – (–1)

–6

3= –2=

b = 1

y = –2x + 1

y = mx + b


Write an equation in slope intercept form ( y = mx + b)

• Use the points (3,3) and (5,7)• First find the slope using the formula.• The slope is 2.• Now, choose a point so that you can

substitute for x, y, AND m to be able to find b.• 3 = 2 ( 3) + b solve for b.• B is –3• So the equation is y = 2x - 3


Summarizer and Review!Graph an equation in slope-intercept form.

y = –2x + 1 m = –2; b = 1

Graph the y-intercept (0, 1).

Move 1 unit right and 2 units down to locate

(1, –1). Draw the line through (0,

1) and (1, –1).TOC


Intercepts• When finding the x-intercept, y=0• When finding the y-intercept, x=0• Example y= 4x – 5• Find the x and y intercepts:


Finding the x-intercept• Remember the x-intercept is where the line

crosses the x-axis• What can you tell me about ANY x intercept?• What is the x-intercept of this line?


Do this:• Y= -3x + 12• Find the x and y intercepts. ( y is easy!)• Y intercept is 12 (0, 12)• To find the x intercept , substitute 0 for y.

• So the x intercept is 4 (4, 0)

• Note: y intercepts always have a 0 for x• Note: x intercepts always have a 0 for y


Try Another!• Y = 2x – 18• Find the x and y intercepts• Y = -18• The ordered pair is (0,-18)• Find the x intercept (sub. 0 in for y)• 0 = 2x – 18• X =9• The ordered pair is (9,0)


Try these• Find the intercepts for• Y = -4x + 8• The intercepts are (0,8) and (2,0)

• Y= 3x – 15• The intercepts are (0,-15) and (5,0)


Writing equations for Horizontal Lines

• Consider the slope intercept form of a line• Y = mx +b• What is the slope (m) of a horizontal line?• 0• So we know m is going to be zero.

• Y = 0(x) + b• Y = b (use this for any horizontal line!)


Lets try!

What is b (the y-intercept of this line)?

B is 4.

Y=4 is your equation.


Same idea applies for vertical lines

What is the x-intercept of this line? 3!

X=3 is the equation!

Remember, the slope of a vertical line is undefined!


Write the equations for these lines.

Y=-3 X = -2


Summarizer• How can you determine the equation of a line

if all you see is the graph?

• Find the y-intercept and let be “b”.• Calculate rise/run to determine the slope “m”

• Write in the from Y=mx + b


HomeworkWork book pg. 17-19, #’s 1-33 all


HW Answers:1. 5; 5

2. 2; -3

3. 5; -2

4. -3; 1

5. -4; -3

6. 1; 5

7. 9

8. 4

9. -1

10. 5

11. -18

12. 7

13. 6

14. -5

15. 10/9

16. -7

17. -11

18. 6


19. 6

20. -7

21. 8

22. 4

23. 3

24. -3

25-27 Graphs

28. c

29. B

30. A

31-33 Graphs

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Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Slope-Intercept Form A.CED.2