Answer
$\color{blue}{y=-1.75x+9}$
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 $(3, 3.75)$ and $(6, -1.5)$:
\begin{align*}
m&=\frac{y_2-y_1}{x_2-x_1}\\
m&=\frac{-1.5-3.75}{6-3}\\\\
m&=\frac{-5.25}{3}\\\\
m&=-1.75
\end{align*}
Hence, the tentative equation fo the line that contains the given points is:
$$y=-1.75x+b$$
Solve for the $b$ by substituting the $x$ and $y$ values of the point $(3, 3.75)$ into the tentative equation above to obtain:
\begin{align*}
y&=-1.75x+b\\
3.75&=-1.75(3)+b\\
3.75&=-5.25+b\\
3.75+5.25&=b\\
9&=b\\
\end{align*}
Therefore, the equation of the line that contains the given points in the table is $\color{blue}{y=-1.75x+9}$.
