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Graphing inequalities Lesson 14 Warm Ups Lesson 14 At both Quick Car Rental and Speedy Car Rental, the cost, in dollars, of renting a full size car depends on a fixed daily rental fee and a fixed charge per mile that the car is driven. However, the daily rental fee and the charge per mile are not the same for the 2 companies. In the graph below, line Q represents the total cost for quick car rental and line S represents the total cost for speedy car rental $60 Q $50 S 1. Robert plans to rent a full-size car for 1 day and drive 50 miles. Which company will be cheaper, and how much will he save? 2. If y rent a full size car from quick car rental for 1 day, how much more would the total rental cost be if you drove the car 78 miles than if you drove it 77 miles? $40 $30 $20 3. What would be the total cost of renting a full size car from Speedy Car Rental for 1 day and driving the car 150 miles? $10 0 0 20 40 60 80 100 miles Putting inequality in slope intercept form Solve the following inequality for y Move everything except y over to the right. Get rid of the coefficient of y (multiply or divide) 2x - 2y + 6 > 4 3x - 6y + 6 > 12 -2x - 6 -6 – 2x -3x - 6 -6 - 3x -2y > -2 – 2x -6y > 6 – 3x -2y -2 y -6y > 6 – 3x > -2 – 2x -2 -6y > 6 – 3x <1 + x -6 y -6 <-1 + ½ x Solve like a 2 variable equations except when you multiply or divide by a negative. Solve the following inequalities 1. 2x + 4y < 16 y<-½x+4 3. 4x – 5y ≤ -15 y ≥ 4/ 5 x + 3 5. 2x + 4y > - 6 y > - 1/ 2 x – 3/ 2 2. 3y – 6x > -9 y > 2x - 3 4. 2(2x -3y) ≥ 12 y ≤ 2/ 3 x - 2 6. 3y -2(x + 4) < -15 y < 2/ 3 x – 7/ 3 Graphing inequalities Graph the following equation -4x + 2y < 2 1. Solve for y y 2y < 4x + 2 • y<2x+1 2. Determine m (slope) of the equation and b (y-intercept • m=2 b=1 x • 3. Graph the y intercept. 4. Using the slope fine 2 more points. 5. Draw a line through the points. Use a dashed line if the inequality is < or >. 6. Fill in the side of the line that makes the equation true. Graphing inequalities Graph the following equation 1. Solve for y y≤x+2 2. Determine m (slope) of the equation and b (y-intercept 3. Graph the y intercept. y≤x+2 y m=1 • b=2 • • Try (1,1) x y≤x+2 1≤1+2 1 ≤ 3 which is true 4. Using the slope fine 2 more points. 5. Draw a line through the points. Use a dashed line if the inequality is < or >. 6. Fill in the side of the line that makes the equation true. Solving system of inequalities y < 5/4x – 2 2(x + y) ≥ 5 1. Solve for y on 1st equation y < 5/4x - 2 2. Determine m (slope) of the equation and b (y-intercept 3. Graph the y intercept. y m = 5/4 • b = -2 Try (1,1) x y < 5/4x - 2 1≤ 5/ 4 • -2 1 ≤ -3/4 which is false 4. Using the slope fine 2 more points. 5. Draw a line through the points. Use a dashed line if the inequality is < or >. •6. Fill in the side of the line that makes the equation true. Graphing inequalities 7. Solve for y 2nd equation 2(x + y) ≥ 5 2x + 2y ≥ 5 2y ≥ -2x + 5 8. Determine m (slope) of the equation and b (y-intercept m = -1 b = 5/2 9. Graph the y intercept. y y ≥- x + 5/2 • • • Try (1,1) x 2(x + y) ≥ 5 2(1 + 1) ≥ 5 2(2) ≥ 5 4 ≥ 5 which is false 10. Using the slope fine 2 more points. 11. Draw a line through the points. Use a dashed line if the inequality is < or >. 12. Fill in the side of the line that makes the equation true. Homework Lesson 14