Answer
$\color{blue}{y=-2.5x+17}$
Work Step by Step
Recall:
(1) The slope $m$ of a line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula
$$m=\dfrac{y_2-y_1}{x_2-x_1}$$
(2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the $y$-intercept.
Solve for the slope of the line using the formula above and the points $(4, 7)$ and $(14, -18)$:
\begin{align*}
m&=\frac{y_2-y_1}{x_2-x_1}\\
m&=\frac{-18-7}{14-4}\\\\
m&=\frac{-25}{10}\\\\
m&=-2.5
\end{align*}
Hence, the tentative equation fo the line that contains the given points is:
$$y=-2.5x+b$$
Solve for the $b$ by substituting the $x$ and $y$ values of the point $(4, 7)$ into the tentative equation above to obtain:
\begin{align*}
y&=-2.5x+b\\
7&=-2.5(4)+b\\
7&=-10+b\\
7+10&=b\\
17&=b\\
\end{align*}
Therefore, the equation of the line that contains the given points in the table is $\color{blue}{y=-2.5x+17}$.
