Answer
$y=\frac{1}{2}x+8$
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{11-9}{6-2}\\\\
m&=\dfrac{2}{4}\\\\
m&=\frac{1}{2}
\end{align*}
The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$=y-intercept.
With $m=\frac{1}{2}$, the tentative equation of the line through the two given points is $y=\frac{1}{2}x+b$.
(2) To find the value of $b$, substitute the $x$ and $y$ values of the point $(2, 9)$ into the tentative equation above to obtain:
\begin{align*}
y&=\frac{1}{2}x+b\\
9&=\frac{1}{2}(2)+b\\
9&=1+b\\
9-1&=b\\
8&=b
\end{align*}
Therefore, the equation of the line passing through the two given points is:
$$y=\frac{1}{2}x+8$$
