Question

8. The fuel economy of a car in miles per gallon (mpg) depends on the speed the car is traveling. A car's fuel economy in the city per x gallons of gas is represented by y = 22x. A car's fuel economy on the highway is shown in the graph below. 400 320 240 , Distance (miles) 80 2 6 10 Amount of Gas (gallons) Does the car have better fuel economy in the city or on the highway? How much better?

Answer 1

The car has a better fuel economy on the highway

It is better by 18 units

Here in this question, we want to compare the fuel economy in both locations

Since we already have an expression for the economy in the city, we need to get for the highway

As we can see, the fuel economy is a linear relationship between distance and amount of gas. What this mean is that we can establish a linear model for the fuel economy

The general equation of a staright line is;

`y\text{ = mx + b}`

where m is the slope and b is the y-intercept

From what we have for the model in the city, we can deduce that the slope is 22 and thus that is the fuel economy for the city

For the highway, we need to calculate the slope of the linear model

To do this, we select any two points and apply the slope equation

We have this as;

`m\text{ = }\frac{y_{2_{}}-y_1}{x_{2_{}}-x_1}`

The two selected points from the plot are (2,80) and (6,240)

The slope is thus calculated as;

`m\text{ = }(240-80)/(6-2)=(160)/(4)\text{ = 40}`

As we can see from the calculation, the fuel economy on the highway is 40

This is bigger than what we have in the city

By what amount?

That would be 40-22 = 18