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Warm-Up

1. . (-5, -6), m = 3. ANSWER. 2 x + y = – 4. ANSWER. – 2 x + y = 5. Warm-Up. Write an equation in standard form of the line that passes through the given point and has the given slope m or that passes through the two given points. 2. (– 4, – 3), (1, 6).

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Warm-Up

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  1. 1. (-5, -6), m = 3 ANSWER 2x + y = – 4 ANSWER – 2x + y = 5 Warm-Up Write an equation in standard form of the line that passes through the given point and has the given slope m or that passes through the two given points. 2. (– 4, – 3), (1, 6) • Rewrite the equation in standard form with integer coefficients. • a) 0.5x + 0.38y = 0.2 • b) 2.3x + 0.283y = 3.28

  2. 1. (1, – 6), m = – 2 ANSWER 2x- y= – 9 Daily Homework Quiz For use after Lesson 5.6 Write an equation in standard form of the line that passes through the given point and has the given slope m. Rewrite the equation in standard form with integer coefficients. 3.5x + 0.38y = 38 350x + 38y = 3800

  3. a. Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill. Solve a multi-step problem EXAMPLE 5 Library Your class is taking a trip to the public library. You can travel in small and large vans. A small van holds 8 people and a large van holds 12 people. Your class could fill 15 small vans and 2 large vans. b. Graph the equation from part (a). c. List several possible combinations.

  4. 8 s + 12 p l = Solve a multi-step problem EXAMPLE 5 SOLUTION a. Write a verbal model. Then write an equation. Because your class could fill 15 small vans and 2 large vans, use (15, 2) as the s- and l-values to substitute in the equation 8s + 12l=pto find the value of p. Substitute15forsand2forl. 8(15) + 12(2) = p 144 = p Simplify. Substitute 144 for pin the equation 8s+12l = p.

  5. ANSWER The equation 8s+12l=144 models the possible combinations. Solve a multi-step problem EXAMPLE 5 b. Find the intercepts of the graph. Substitute0fors. 8(0) + 12l = 144 l = 12 8s + 12(0) = 144 Substitute 0 for l. 8s + 12(0) = 144 s = 18

  6. c. The graph passes through (0, 12),(6, 8),(12, 4), and (18, 0). So, four possible combinations are 0 small and 12 large,6 small and 8 large,12 small and 4 large,18 small and 0 large. Solve a multi-step problem EXAMPLE 5 Plot the points (0, 12) and (18, 0). Connect them with a line segment. For this problem only nonnegative whole-number values of sandlmake sense. 8s + 12(0) = 144

  7. Solve a multi-step problem EXAMPLE 5 for Example 5 GUIDED PRACTICE Solve a multi-step problem EXAMPLE 5 7.WHAT IF?In Example 5, suppose that 8 students decide not to go on the class trip. Write an equation that models the possible combinations of small and large vans that your class could fill. List several possible combinations.

  8. 8 s + 12 p l = Solve a multi-step problem EXAMPLE 5 for Example 5 GUIDED PRACTICE Solve a multi-step problem EXAMPLE 5 SOLUTION STEP1 Write a verbal model. Then write an equation. 8 students decide not to go on the class trip, so the class could fill 14 small vans and 2 large vans. Because your class could fill 14 small vans and 2 large vans, use (14, 2) as the s- and l-values to substitute in the equation 8s + 12l=pto find the value of p. Substitute14forsand2forl. 8(14) + 12(2) = p 136 = p Simplify. Substitute 136 for pin the equation 8s+12l = p.

  9. 4 l = 11 12 Solve a multi-step problem EXAMPLE 5 for Example 5 GUIDED PRACTICE ANSWER The equation 8s+12l=136 models the possible combinations. STEP2 Find the intercepts of the graph. Substitute0fors. 8(0) + 12l = 136 8s + 12(0) = 144 Substitute 0 for l. 8s + 12(0) = 136 s = 17

  10. 4 Plot the point(0,11 )and(17, 0).connect them with a line segment. For this problem only negative whole-number values of sandl make sense. 12 for Example 5 GUIDED PRACTICE STEP3 The graph passes through (17, 0),(14, 2), (11, 4),(8, 6), (5, 8) and (2, 10). So, several combinations are 17 small, 0 large;14 small 2 large; 11 small, 4 large;18 small, 6 large;5 small, 8 large;2 small, 10 large. 8s + 12(0) = 144

  11. You have $96 to spend on campground activities. You can rent a paddleboat for $8 per hour and a kayak for $6 per hour. Write an equation in standard form that models the possible hourly combinations of activities you can afford. List three possible combinations. 3. ANSWER 8p + 6c = 96; 16 h kayak and 0 h paddleboat;12 h paddleboat and 0 h kayak;6 h paddleboat and 8 h kayak. Daily Homework Quiz For use after Lesson 5.4

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