Answer
$y=9x-10$
Refer to the graph below.
Work Step by Step
Plot each point and connect the points using a line.
Refer to the graph above.
To find the equation of the line, perform the following steps:
(1) Solve for the slope $m$ using the formula $m=\dfrac{y_2-y_1}{x_2-x_1}$:
\begin{align*}
m&=\dfrac{-1-17}{1-3}\\\\
m&=\dfrac{-18}{-2}\\\\
m&=9
\end{align*}
The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$=y-intercept.
With $m=9$, the tentative equation of the line through the two given points is$y=9x+b$.
(2) To find the value of $b$, substitute the $x$ and $y$ values of the point $(3, 17)$ into the tentative equation above to obtain:
\begin{align*}
y&=9x+b\\
17&=9(3)+b\\
17&=27+b\\
17-27&=b\
-10&=b
\end{align*}
Therefore, the equation of the line passing through the two given points is:
$$y=9x-10$$
