Question

fuel efficiency (in miles per gallon) weight (in pounds) (a) for these 24 vehicles, as weight increases, fuel efficiency tends to decrease. (b) for these 24 vehicles, there is a negative correlation between weight and fuel efficiency. (c) using the line of best fit, we would predict that a vehicle weighing 3000 pounds would have a fuel efficiency of approximately select

Explanation:

Step1: Identify two points on the line of best - fit

Let's take two points on the line of best - fit. For example, when weight $x_1 = 1500$ pounds, fuel efficiency $y_1\approx35$ miles per gallon and when weight $x_2 = 4500$ pounds, fuel efficiency $y_2\approx15$ miles per gallon.

Step2: Find the slope of the line of best - fit

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{15 - 35}{4500 - 1500}=\frac{- 20}{3000}=-\frac{1}{150}$.

Step3: Use the point - slope form to find the equation of the line

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(x_1 = 1500,y_1 = 35)$ and $m=-\frac{1}{150}$, we have $y-35=-\frac{1}{150}(x - 1500)$.
Simplify the equation:
\[

$$\begin{align*} y-35&=-\frac{1}{150}x + 10\\ y&=-\frac{1}{150}x+45 \end{align*}$$

\]

Step4: Predict the fuel efficiency for $x = 3000$ pounds

Substitute $x = 3000$ into the equation $y=-\frac{1}{150}x + 45$.
$y=-\frac{1}{150}\times3000+45=- 20 + 45 = 25$ miles per gallon.

Answer:

25 miles per gallon