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.

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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. 1. (-5, -6), m = 3 ANSWER 2x + y = – 4 2. (– 4, – 3), (1, 6) ANSWER – 2x + y = 5 Rewrite the equation in standard form with integer coefficients. a) 0.5x + 0.38y = 0.2 b) 2.3x + 0.283y = 3.28

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. 1. (1, – 6), m = – 2 ANSWER 2x - y = – 9 Rewrite the equation in standard form with integer coefficients. 3.5x + 0.38y = 38 350x + 38y = 3800

EXAMPLE 5 Solve a multi-step problem 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. Write an equation in standard form that models the possible combinations of small vans and large vans that your class could fill. a. b. Graph the equation from part (a). c. List several possible combinations.

Solve a multi-step problem EXAMPLE 5 Solve a multi-step problem SOLUTION a. Write a verbal model. Then write an equation. 8 s l p 12 + = 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 = p to find the value of p. 8(15) + 12(2) = p Substitute 15 for s and 2 for l. 144 = p Simplify. Substitute 144 for p in the equation 8s + 12l = p.

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

EXAMPLE 5 Solve a multi-step problem Plot the points (0, 12) and (18, 0). Connect them with a line segment. For this problem only nonnegative whole-number values of s and l make sense. 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. c. 8s + 12(0) = 144

EXAMPLE 5 Solve a multi-step problem GUIDED PRACTICE for Example 5 EXAMPLE 5 Solve a multi-step problem 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.

Solve a multi-step problem GUIDED PRACTICE for Example 5 EXAMPLE 5 SOLUTION STEP 1 Write a verbal model. Then write an equation. 8 s l p 12 + = 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 = p to find the value of p. 8(14) + 12(2) = p Substitute 14 for s and 2 for l. 136 = p Simplify. Substitute 136 for p in the equation 8s + 12l = p.

EXAMPLE 5 Solve a multi-step problem GUIDED PRACTICE for Example 5 ANSWER The equation 8s + 12l = 136 models the possible combinations. STEP 2 Find the intercepts of the graph. Substitute 0 for s. 8(0) + 12l = 136 l = 11 4 12 8s + 12(0) = 144 Substitute 0 for l. 8s + 12(0) = 136 s = 17

GUIDED PRACTICE for Example 5 Plot the point(0,11 )and(17, 0).connect them with a line segment. For this problem only negative whole-number values of s and l make sense. 4 12 STEP 3 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

Daily Homework Quiz For use after Lesson 5.4 3. 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. 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.