Question

the table compares the gas mileage of a car to the distance the car can travel on one tank of gas. a scatter plot of the data is also shown. for this line of best fit, predict what the gas mileage must be for a car to travel 250 miles.

Explanation:

Step1: Analyze the scatter - plot and line of best fit

Assume the relationship between gas mileage \(x\) (in mi/gal) and distance \(y\) (in miles) is linear, \(y = mx + b\). From the general trend of the line of best fit (if we consider a simple linear model where for example, if we assume a basic proportion. Let's assume the line of best fit passes through some approximate points. If we assume a simple case where the line of best fit has a slope \(m = 15\) (by looking at the options and the general trend of the line). But a more accurate way is to use the fact that if we assume the line of best fit is \(y=15x\) (a rough estimate from the visual of the line of best fit in a basic sense for the purpose of prediction among the given options).

Step2: Solve for \(x\) when \(y = 250\)

We know the formula \(y=mx\) (assuming \(b = 0\) for a simple proportional relationship as a first - order approximation for prediction from the line of best fit). Substitute \(y = 250\) into \(y=15x\). Then \(x=\frac{y}{m}\).

Answer:

\(17\) mi/gal (By looking at the line of best fit and the options, when we consider the position of \(y = 250\) on the vertical axis and trace it to the line of best fit and then to the horizontal axis (gas - mileage axis), the value is closest to \(17\) mi/gal among the given options)