2. Main Idea and New Vocabulary Example 1: Find Slopes and y-intercepts
Example 3: Write an Equation in Slope-Intercept Form
Example 4: Write an Equation in Slope-Intercept Form
Example 5: Graph Using Slope-Intercept Form
Example 6: Graph an Equation to Solve Problems
Example 7: Graph an Equation to Solve Problems
Lesson Menu

3. Graph linear equations using the slope and y-intercept.
slope-intercept form
y-intercept
Main Idea/Vocabulary

4. Find Slopes and y-intercepts
State the slope and y-intercept of the graph of y = x – 5.
Write the equation in the form y = mx + b.
Answer: The slope of the graph is , and the y-intercept is −5.
Example 1

5. State the slope and y-intercept of the graph of .
A. slope: ; y-intercept: 1
B. slope: ; y-intercept: 1
C. slope: 1; y-intercept:
D. slope: 1; y-intercept:
Example 1 CYP

6. Find Slopes and y-intercepts
State the slope and y-intercept of the graph of 2x + y = 8.
2x + y = 8 Write the original equation.
2x – 2x + y = 8 – 2x Subtract 2x from each side.
y = 8 − 2x Simplify.
y = −2x + 8 Write the equation in the form y = mx + b.
y = mx + b m = –2, b = 8
Answer: The slope of the graph is –2 and the y-intercept is 8.
Example 2

7. State the slope and y-intercept of the graph of y – 4x = 10.
A. slope: –4; y-intercept: 10
B. slope: 4; y-intercept: 10
C. slope: 10; y-intercept: –4
D. slope: 10; y-intercept: 4
Example 2 CYP

8. Write an Equation in Slope-Intercept Form
Write an equation of a line in slope-intercept form with a slope of 2 and a y-intercept of –8.
y = mx + b Slope-intercept form
y = 2x + (–8) Replace m with 2 and b with –8.
y = 2x – 8 Simplify.
Answer: y = 2x – 8
Example 3

9. Write an equation of a line in slope-intercept form with a slope of – and a y-intercept of 6.
A. y = – x – 6
B. y = – x + 6
C. y = x + 6
D. y = 6x –
Example 3 CYP

10. Write an Equation in Slope-Intercept Form
Write an equation in slope-intercept form for the graph shown.
The y-intercept is 1. From (0, 1), you move up 2 units and left 3 units to another point on the line.
So, the slope is – .
Example 4

11. Write an Equation in Slope-Intercept Form
y = mx + b Slope-intercept form
y = – x + 1 Replace m with – and b with 1.
y = – x + 1
Answer: y = – x + 1
Example 4

12. Write an equation in slope-intercept form for the graph shown.
A. y = –3x – 2
B. y = 3x – 2
C. y = – x – 1
D. y = x – 1
Example 4 CYP

13. Graph Using Slope-Intercept Form
Graph using the slope and y-intercept.
Step 1 Find the slope and y-intercept.
y = x slope = , y-intercept = 2
Example 5

14. Graph Using Slope-Intercept Form
Step 2 Graph the y-intercept 2.
Example 5

15. Graph Using Slope-Intercept Form
Step 3 Use the slope to locate a second point on the line.
←change in y: up 2 units ←change in x: right 3 units
m =
Example 5

16. Graph Using Slope-Intercept Form
Step 4 Draw a line through the two points.
Answer:
Example 5

17. Graph y = – x + 3 using the slope and y-intercept.
A. B.
C. D.
Example 5 CYP

18. Graph an Equation to Solve Problems
KAYAK RENTAL A kayak rental pavilion charges $15.00 per hour and $2.50 for instruction on how to not fall out of the kayak. The total cost is given by the equation y = 15x + 2.5, where x is the number of hours the kayak is rented. Graph the equation to find the total cost for 2 hours.
y = 15x slope = 15, y-intercept = 2.5
Example 6

19. Graph an Equation to Solve Problems
Plot the point (0, 2.5).
Locate another point up 15 and right 1.
Draw the line.
The y-coordinate is 32.5 when the x-coordinate is 2, so the total cost for 2 hours is $32.50.
Answer: The total cost for 2 hours is $32.50.
Example 6

20. POTTERY A pottery studio charges $16 per hour and $10 for firing fees
POTTERY A pottery studio charges $16 per hour and $10 for firing fees. The total cost is given by the equation y = 16x + 10, where x is the number of hours a customer uses the studio. Graph the equation to find the total cost for 5 hours.
A. $26
B. $80
C. $90
D. $100
Example 6 CYP

21. Graph an Equation to Solve Problems
KAYAK RENTAL A kayak rental pavilion charges $15.00 per hour and $2.50 for instruction on how to not fall out of the kayak. The total cost is given by the equation y = 15x + 2.5, where x is the number of hours the kayak is rented. Interpret the slope and the y-intercept.
Example 7

22. Graph an Equation to Solve Problems
Answer: The slope 15 represents the rate of change or cost per hour. The y-intercept 2.5 is the charge for instruction.
Example 7

23. POTTERY A pottery studio charges $16 per hour and $10 for firing fees
POTTERY A pottery studio charges $16 per hour and $10 for firing fees. The total cost is given by the equation y = 16x + 10, where x is the number of hours a customer uses the studio. Interpret the slope and the y-intercept.
A. The slope 10 represents the firing fee. The y-intercept 16 is the cost per hour.
B. The slope 10 represents the cost per hour. The y-intercept 16 is the firing fee.
C. The slope 16 represents the firing fee. The y-intercept 10 is the cost per hour.
D. The slope 16 represents the cost per hour. The y-intercept 10 is the firing fee.
Example 7 CYP