Answer
Model: $ y = 2.5x-7$
Domain: All real numbers
Range: All real numbers
Work Step by Step
First make a scatter plot to determine the model type. Our scatter plot shows that the data is linear. Therefore find the slope of the line using any two points in the table.
$$\begin{aligned}
m&= \frac{y_2-y_1}{x_2-x_1}\\
&= \frac{8-3}{6-4}\\
&= \frac{5}{2}\\
&= 2.5
\end{aligned}$$ Find the equation of the line. Use $(0,-7)$: $$\begin{aligned}
y-y_1&= m(x-x_1)\\
y+7&= 2.5(x-0)\\
y&= 2.5x-7.
\end{aligned}$$ Hence the model is $$ y = 2.5x-7.$$ The domain and range are:
Domain: All real numbers
Range: All real numbers
