Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
1-3. Quiz
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Exercise 16 Page 184

Find the rate of change for consecutive data pairs.

Can the Situtaion Be Modeled by a Linear Equation? Yes.
Equation: y=-2.5x+175

Practice makes perfect

Let's find the rate of change for the consecutive data pairs in the table.

Points y_2-y_1/x_2-x_1 m
(14,140), (16,135) 135-140/16-14 -2.5
(12,145), (14,140) 140-145/14-12 -2.5
(10,150), (12,145) 145-150/12-10 -2.5
(8,155), (10,150) 150-155/10-8 -2.5
Since the rate of change is constant, the data in the table can be modeled by a linear equation with a slope of -2.5. Using one of the points, let's say ( 8, 155), we can write a linear model in Point-Slope Form. y- 155= -2.5(x- 8) In this model, x is time in minutes and y is the amount of water in the tank in gallons. Since we are asked to express the amount of water as a function of time, we need to solve this equation for y.

y-155=-2.5(x-8)
y-155=-2.5x+20
y=-2.5x+175

Therefore, after x minutes there are y=-2.5x+175 gallons of water in the tank.