Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 42

Determine the slope of the line.







Based from the graph, the line passed through points $(1,-1)$ and $(4,5)$. The slope of the line is

We let $(1,-1) = (x_1,y_1)$ and $(4,5) = (x_2, y_2)$ in the slope formula


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-1)}{4 - 1}
&& \text{Substitute } (x_1,y_1) = (1,-1) \text{ and } (x_2, y_2) = (4,5)
\\
\\
=& \frac{6}{3}
&& \text{Simplify}
\\
\\
=& 2
&&

\end{aligned}
\end{equation}
$


Thus, the slope is $2$.