Answer
$\color{blue}{y=\dfrac{7}{2}x-4}$
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.
The table shows that the line passes through the point $(0, -4)$. This means that $b=-4$.
Hence, the tentative equation fo the line that contains the given points is:
$$y=mx-4$$
The line also contains the point $(4, 10)$.
Substitute the $x$ and $y$ values of this point into the tentative equation above to obtain:
\begin{align*}
y&=mx-4\\
10&=m(4)-4\\
10+4&=4m\\
14&=4m\\
\frac{14}{4}&=m\\
\frac{7}{2}&=m
\end{align*}
Therefore, the equation of the line that contains the given points in the table is $\color{blue}{y=\frac{7}{2}x-4}$.
