2. Main Idea and New Vocabulary NGSSS
Example 1: Find Slopes and y-intercepts
Example 2: 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
Five-Minute Check
Lesson Menu

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

4. MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem.
NGSSS

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

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

16. 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

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

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

19. 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. State the slope and the y-intercept for the graph of the equation y = 2x + 1.
A. m = ; b = 1
B. m = 1; b = 2
C. m = 2; b = –
D. m = 2; b = 1
Five Minute Check 1

26. State the slope and the y-intercept for the graph of the equation y = 3x + 2.
A. m = –2; b = 3
B. m = 2; b = 3
C. m = 3; b = –2
D. m = 3; b = 2
Five Minute Check 2

27. State the slope and the y-intercept for the graph of the equation y = −2x + 4.5.
A. m = −4.5; b = –2
B. m = −2; b = 4.5
C. m = 2; b = 4.5
D. m = 4.5; b = –2
Five Minute Check 3

28. State the slope and the y-intercept for the graph of the equation 3x − y = 4.
A. m = 3; b = −4
B. m = –3; b = −4
C. m = 3; b = 4
D. m = −4; b = 3
Five Minute Check 4

29. A. the total price of apples B. the price of apples per pound
The total price of apples y at an orchard can be calculated with the equation 1.12x + 5 = y, where x is the number of pounds of apples picked. What does the slope represent?
A. the total price of apples
B. the price of apples per pound
C. the number of apples per pound
D. the number of pounds of apples picked
Five Minute Check 5

30. What is the equation of the graph?
A. y = 2x –
B. y = x + 2
C. y = x − 2
D. y = x – 2
Five Minute Check 6