The gas mileage, m, of a compact car is a linear function of the speed, s, at wh

Question

The gas mileage, m, of a compact car is a linear function of the speed, s, at which the car is driven, for 40s ss 90. For example, from the graph we see that the gas mileage for the compact car is 45 miles per gallon if the car is driven at a speed of 40mph Gas Mileage of a Compact Car 60 50 40 30 20 10 45 40 50 607080 90 Speed (mph) a) Using the two points on the graph, determine the function m(s) that can be used to approximate the graph. b) Using the function from part a, estimate the gas mileage if the compact car is traveling 43 mph. If necessary, round to the nearest tenth. Using the function from part a, estimate the speed of the compact car if the gas mileage is 41 miles per gallon. If necessary, round to the nearest tenth.

Explanation / Answer

As the graph is a linear relation and we know the points on the

Graph with slope m can be found.

a)

Line equation is =

y-y1 = m(x-x1)

(x1,y1) is any point on graph

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

= (40-45)/(50-40)

= -5/10

Slope = -1/2

So, the equation

y-45 = -1/2 (x-40)

2y-90 = -x+40

X = -2y+130

Now replace x,y with speed and mileage

S = -2m+130 is our function.

b)

Given s =43. We need to find m

43 = -2m+130

m = 87/2

m = 43.5 is the answer.

c)

Given, m =41

S = -2(41) +130

S = 48 mph is the answer.

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