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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 + 2.5 slope = 15, y-intercept = 2.5 Example 6

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

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

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

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

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