Question

the fuel efficiency of one type of car is recorded in a scatterplot where the amount of gas used, \\(x\\) (in gallons), is paired with the distance traveled, \\(y\\) (in miles), for various trips. the equation for the line of best fit for the data is \\(y = 28x\\). how can the \\(y\\)-intercept and slope of this line be interpreted?

• the \\(y\\)-intercept is 28, which represents the miles that can be traveled with 1 gallon of gas. the slope is 0, which represents the amount of gas used when 0 miles are traveled.
• the \\(y\\)-intercept is 28, which represents the amount of gas used when 0 miles are traveled. the slope is 0, which represents the miles that can be traveled with 1 gallon of gas.
• the \\(y\\)-intercept is 0, which represents the number of miles that can be traveled with 1 gallon of gas. the slope is 28, which represents the amount of gas used when 0 miles are traveled.
• the \\(y\\)-intercept is 0, which represents the amount of gas used when 0 miles are traveled. the slope is 28, which represents the miles that can be traveled with 1 gallon of gas.

Explanation:

Identify the slope and y-intercept from the equation

$$ y = 28x + 0 $$

$$ \text{Slope } (m) = 28 $$

$$ y\text{-intercept } (b) = 0 $$

Interpret the y-intercept in context

$$ x = 0 \implies y = 0 $$

The \(y\)-intercept is \(0\), representing \(0\) miles traveled when \(0\) gallons of gas are used.

Interpret the slope in context

$$ m = \frac{\Delta y}{\Delta x} = 28 \text{ miles per gallon} $$

The slope is \(28\), representing the number of miles that can be traveled with \(1\) gallon of gas.

Answer:

• The y-intercept is 28, which represents the miles that can be traveled with 1 gallon of gas. The slope is 0, which represents the amount of gas used when 0 miles are traveled.
• The y-intercept is 28, which represents the amount of gas used when 0 miles are traveled. The slope is 0, which represents the miles that can be traveled with 1 gallon of gas.
• The y-intercept is 0, which represents the number of miles that can be traveled with 1 gallon of gas. The slope is 28, which represents the amount of gas used when 0 miles are traveled.
• The y-intercept is 0, which represents the amount of gas used when 0 miles are traveled. The slope is 28, which represents the miles that can be traveled with 1 gallon of gas. (Correct answer)