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Objective - To solve word problems involving linear situations. Three types of word problems 1) Point/Slope 2) Two Points 3) Two Things and a Total Point - Slope Problem A water tank contains 600 gallons of water and is leaking at a rate of 15 gal/min. Write a linear equation representing the tank volume in terms of time. Let x = # minutes Let y = volume in gallons y 600 15x Two Points The volume in a water tank after 10 minutes is 450 gallons. After 30 minutes, the volume in the tank is 150 gallons. Write an equation representing the volume in terms of time. Let x = # minutes Let y = volume in gallons x1, y1 10,450 x 2 , y2 30,150 Two Things and a Total Sandwiches cost $3 each and sodas cost $2 each. If Sam spent a total of $24, how many of each could he have bought? Let x = # of sandwiches Let y = # of sodas 3x 2y 24 Write a linear equation to describe each situation. Point and Slope A sky diver jumps from a plane at 11,000 ft. above the ground and descends at 15 ft./sec. y = height (ft.) x = time (sec.) Start Value = b = 11,000 Change = m = -15 Two Points A sky diver jumps from a plane. He is 10,100 ft. above the ground after 60 sec. and is 8300 ft. after 3 min. (x1 , y1 ) (60, 10,100) (x 2 , y 2 ) (180, 8300) A masonry company charges $0.80 a brick. The company will charge $465 for 500 bricks to be delivered to a site. If x = the number of bricks, and y = total cost, write an equation for y in terms of x. Slope Change in price = $0.80/ brick m = 0.80 Point 500 bricks cost $465 (x, y) = (500, 465) y = mx + b y = 0.80x + b 465 = 0.8(500) + b 465 = 400 + b -400 -400 65 = b y = 0.8x + 65 Suppose a 5 minute call costs $6.20 and a 20 minute call costs $18.05. Write an equation which describes cost y in terms of x minutes. (minutes, cost) (x, y) (5, 6.20) (20, 18.05) y2- y 1 m= = 18.05 - 6.20 x2- x 1 20 - 5 m = 11.85 = 0.79 15 y = 0.79x + 2.25 y = mx + b y = 0.79x + b 6.20 = 0.79(5) + b 6.20 = 3.95 + b -3.95 -3.95 2.25 = b r = -3p +12 m = -3 b = 12 # Rulers Pens cost $3 each and rulers cost $1 each. If Jim spends $12, how many of each did he buy? Let p = # of pens purchased Let r = # of rulers purchased 12 3p + 1r = 12 -3p -3p 10 1r = -3p +12 8 6 4 2 0 1 2 3 # Pens 4 5