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

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

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

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

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

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

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

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

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

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