11 3 Using Slopes and Intercepts Warm Up

11 -3 Using Slopes and Intercepts Warm Up Problem of the Day Lesson Presentation Course 3

11 -3 Using Slopes and Intercepts Warm Up Find the slope of the line that passes through each pair of points. 1. (3, 6) and (-1, 4) 1 2 -1 5 3. (4, 6) and (2, -1) 7 2 4. (-3, 0) and (-1, 1) 1 2 2. (1, 2) and (6, 1) Course 3

11 -3 Using Slopes and Intercepts Problem of the Day Write the equation of a straight line that passes through fewer than two quadrants on a coordinate plane. x = 0 or y = 0 Course 3

11 -3 Using Slopes and Intercepts Learn to use slopes and intercepts to graph linear equations. Course 3

11 -3 Using Insert. Slopes Lessonand Title Here Intercepts Vocabulary x-intercept y-intercept slope-intercept form Course 3

11 -3 Using Slopes and Intercepts You can graph a linear equation easily by finding the x-intercept and the y-intercept. The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0). Course 3

11 -3 Using Slopes and Intercepts Additional Example 1: Finding x-intercepts and y-intercepts to Graph Linear Equations Find the x-intercept and y-intercept of the line 4 x – 3 y = 12. Use the intercepts to graph the equation. Find the x-intercept (y = 0). 4 x – 3 y = 12 4 x – 3(0) = 12 4 x= 12 4 4 x=3 The x-intercept is 3. Course 3

11 -3 Using Slopes and Intercepts Additional Example 1 Continued Find the y-intercept (x = 0). 4 x – 3 y = 12 4(0) – 3 y = 12 -3 y= 12 -3 -3 y = – 4 The y-intercept is – 4. Course 3

11 -3 Using Slopes and Intercepts Additional Example 1 Continued The graph of 4 x – 3 y = 12 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, – 4). Course 3

11 -3 Using Slopes and Intercepts Try This: Example 1 Find the x-intercept and y-intercept of the line 8 x – 6 y = 24. Use the intercepts to graph the equation. Find the x-intercept (y = 0). 8 x – 6 y = 24 8 x – 6(0) = 24 8 x= 24 8 8 x=3 The x-intercept is 3. Course 3

11 -3 Using Slopes and Intercepts Try This: Example 1 Continued Find the y-intercept (x = 0). 8 x – 6 y = 24 8(0) – 6 y = 24 -6 y= 24 -6 -6 y = – 4 The y-intercept is – 4. Course 3

11 -3 Using Slopes and Intercepts Try This: Example 1 Continued The graph of 8 x – 6 y = 24 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, – 4). Course 3

11 -3 Using Slopes and Intercepts In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept. y = mx + b Slope Course 3 y-intercept

11 -3 Using Slopes and Intercepts Helpful Hint For an equation such as y = x – 6, write it as y = x + (– 6) to read the y-intercept, – 6. Course 3

11 -3 Using Slopes and Intercepts Additional Example 2 A: Using Slope-Intercept Form to Find Slopes and y-intercepts Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 2 x + y = 3 – 2 x Subtract 2 x from both sides. y = 3 – 2 x Rewrite to match slope-intercept form. y = – 2 x + 3 The equation is in slope-intercept form. m = – 2 b = 3 The slope of the line 2 x + y = 3 is – 2, and the y-intercept is 3. Course 3

11 -3 Using Slopes and Intercepts Additional Example 2 B: Using Slope-Intercept Form to Find Slopes and y-intercepts B. 5 y = 3 x 5 y= 3 x Divide both sides by 5 to solve for y. 5 5 y =3 x + 0 The equation is in slope-intercept form. 5 m =3 5 b=0 The slope of the line 5 y = 3 x is 3 , and the 5 y-intercept is 0. Course 3

11 -3 Using Slopes and Intercepts Additional Example 2 C: Using Slope-Intercept Form to Find Slopes and y-intercepts C. 4 x + 3 y = 9 – 4 x Subtract 4 x from both sides. 3 y = 9 – 4 x Rewrite to match slope-intercept form. 3 y = – 4 x + 9 3 y= – 4 x +9 Divide both sides by 3. 3 3 3 y =- 4 3 x + 3 The equation is in slope-intercept form. The slope of the line 4 x+ 3 y = 9 is 4 m =- 4 b = 3 – , 3 and the y-intercept is 3. 3 Course 3

11 -3 Using Slopes and Intercepts Try This: Example 2 A Write each equation in slope-intercept form, and then find the slope and y-intercept. A. 4 x + y = 4 – 4 x Subtract 4 x from both sides. y = 4 – 4 x Rewrite to match slope-intercept form. y = – 4 x + 4 The equation is in slope-intercept form. m = – 4 b = 4 The slope of the line 4 x + y = 4 is – 4, and the y-intercept is 4. Course 3

11 -3 Using Slopes and Intercepts Try This: Example 2 B B. 7 y = 2 x 7 y= 2 x Divide both sides by 7 to solve for y. 7 7 y =2 x + 0 The equation is in slope-intercept form. 7 m =2 7 b=0 The slope of the line 7 y = 2 x is 2 , and the 7 y-intercept is 0. Course 3

11 -3 Using Slopes and Intercepts Try This: Example 2 C C. 5 x + 4 y = 8 – 5 x Subtract 5 x from both sides. 4 y = 8 – 5 x Rewrite to match slope-intercept form. 5 x + 4 y = 8 4 y= – 5 x +8 Divide both sides by 4. 4 4 4 y =- 5 The equation is in slope-intercept form. 4 x + 2 The slope of the line 5 x + 4 y = 8 is 5 m =- 5 b = 2 – , 4 and the y-intercept is 2. 4 Course 3

11 -3 Using Slopes and Intercepts Additional Example 3: Entertainment Application A video club charges $8 to join, and $1. 25 for each DVD that is rented. The linear equation y = 1. 25 x + 8 represents the amount of money y spent after renting x DVDs. Graph the equation by first identifying the slope and y-intercept. y = 1. 25 x + 8 m =1. 25 Course 3 The equation is in slope-intercept form. b=8

11 -3 Using Slopes and Intercepts Additional Example 3 Continued The slope of the line is 1. 25, and the y-intercept is 8. The line crosses the y -axis at the point (0, 8) and moves up 1. 25 units for every 1 unit it moves to the right. Course 3

11 -3 Using Slopes and Intercepts Try This: Example 3 A salesperson receives a weekly salary of $500 plus a commission of 5% for each sale. Total weekly pay is given by the equation S = 0. 05 c + 500. Graph the equation using the slope and y-intercept. y = 0. 05 x + 500 m =0. 05 Course 3 The equation is in slope-intercept form. b = 500

11 -3 Using Slopes and Intercepts Try This: Example 3 Continued y The slope of the line is 0. 05, and the y-intercept is 500. The line crosses the y-axis at the point (0, 500) and moves up 0. 05 units for every 1 unit it moves to the right. 2000 1500 1000 500 x 5000 10, 000 15, 000 Course 3

11 -3 Using Slopes and Intercepts Additional Example 4: Writing Slope-Intercept Form Write the equation of the line that passes through (3, – 4) and (– 1, 4) in slope-intercept form. Find the slope. y 2 – y 1 4 – (– 4) = 8 = – 2 = x 2 – x 1 – 4 – 1 – 3 The slope is – 2. Choose either point and substitute it along with the slope into the slope-intercept form. y = mx + b 4 = – 2(– 1) + b Substitute – 1 for x, 4 for y, and – 2 for m. 4=2+b Course 3 Simplify.

11 -3 Using Slopes and Intercepts Additional Example 4 Continued Solve for b. 4=2+b – 2 2=b Subtract 2 from both sides. Write the equation of the line, using – 2 for m and 2 for b. y = – 2 x + 2 Course 3

11 -3 Using Slopes and Intercepts Try This: Example 4 Write the equation of the line that passes through (1, 2) and (2, 6) in slope-intercept form. Find the slope. y 2 – y 1 6– 2 = 4 =4 = x 2 – x 1 1 2– 1 The slope is 4. Choose either point and substitute it along with the slope into the slope-intercept form. y = mx + b 2 = 4(1) + b Substitute 1 for x, 2 for y, and 4 for m. 2=4+b Simplify. Course 3

11 -3 Using Slopes and Intercepts Try This: Example 4 Continued Solve for b. 2=4+b – 4 – 2 = b Subtract 4 from both sides. Write the equation of the line, using 4 for m and – 2 for b. y = 4 x – 2 Course 3

11 -3 Using Insert Slopes Lessonand Title Intercepts Here Lesson Quiz Write each equation in slope-intercept form, and then find the slope and y-intercept. 1. 2 y – 6 x = – 10 y = 3 x – 5; m = 3; b = – 5 2. – 5 y – 15 x = 30 y = – 3 x – 6; m = – 3; b = – 6 Write the equation of the line that passes through each pair of points in slopeintercept form. 3 3. (0, 2) and (4, – 1) y = – 4 x + 2 4. (– 2, 2) and (4, – 4) y = –x Course 3