2. Lesson Menu Main Idea and New Vocabulary 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

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

4. Example 1 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.

5. Example 1 CYP 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:

6. Example 2 State the slope and y-intercept of the graph of 2x + y = 8. Find Slopes and y-intercepts 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.

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

8. Example 3 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 – 8Simplify. Answer: y = 2x – 8

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

10. Example 4 Write an equation in slope-intercept form for the graph shown. Write an Equation in Slope- Intercept Form 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 –.

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

12. Example 4 CYP 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

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

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

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

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

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

18. Example 6 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 + 2.5slope = 15, y-intercept = 2.5 Graph an Equation to Solve Problems

19. Example 6 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. Graph an Equation to Solve Problems Answer:The total cost for 2 hours is $32.50.

20. Example 6 CYP A.$26 B.$80 C.$90 D.$100 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.

21. Example 7 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. Graph an Equation to Solve Problems

22. Example 7 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.

23. Example 7 CYP 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. 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.