SOLUTION: Highway bridges often have expansion joints- small gaps between the bridge sections-that allow for the expansion of the bridge when the weather gets hot. Suppose that a bridge's ex

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Question 714737: Highway bridges often have expansion joints- small gaps between the bridge sections-that allow for the expansion of the bridge when the weather gets hot. Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75�F and that gap increases to 1 inch when the temperature is 50�F . Assume that there is a linear relationship between the width of the gap and the temperature.
1. Write an equation that expresses the width of the gap (W) as a function of the temperature (T).
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Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let x = gap width in inches and y = temperature in Fahrenheit

"Suppose that a bridge's expansion joint has a gap of 1/2 inches when the temperature if 75�F" means x = 1/2 and y = 75

"and that gap increases to 1 inch when the temperature is 50�F " means x = 1 and y = 50

Let's find the slope of the line through these two points

Slope:

m = (y2 - y1)/(x2 - x1)

m = (50 - 75)/(1 - 1/2)

m = (-25)/(1/2)

m = -50

So the slope is m = -50

Now use this to find the equation

y = mx + b

y = -50x + b ... plug in the slope we just found

50 = -50(1) + b ... plug in x = 1 and y = 50

50 = -50 + b

50 + 50 = b

100 = b

b = 100

So the equation is y = -50x + 100

Replace x with W since x = gap and y with T because y = temp to get

T = -50W + 100

Now solve for W (because we want an equation that expresses the width of the gap (W) as a function of the temperature (T))

So the final answer is