Beginning Algebra With Applications, Chapter 5, Test, Section Test, Problem 2

Determine the slope of the line that contains the points whose coordinates are $(9,8)$ and $(-2,1).$

We let $(x_1, y_1) = (9,8)$ and $(x_2, y_2) = (-2,1)$

Using the formula for the slope of a line


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2 - y_1}{x_2 - x_1}
\\
\\
m =& \frac{1-8}{-2-9} = \frac{-7}{-11} = \frac{7}{11}

\end{aligned}
\end{equation}
$



Then using the point slope formula, where $(x_1, y_1) = (9,8)$ and $\displaystyle m = \frac{7}{11}$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
\\
\\
y - 8 =& \frac{7}{11} (x-9)
\\
\\
y - 8 =& \frac{7}{11}x - \frac{63}{11}
\\
\\
y =& \frac{7}{11}x - \frac{63}{11} + 8
\\
\\
y =& \frac{7}{11}x + \frac{25}{11}

\end{aligned}
\end{equation}
$