Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 48

Determine the slope of of the line $4x - y = 4$ and sketch the graph.

The intercepts can be used as the two different points needed to find the slope. So

$x$-intercepts


$
\begin{equation}
\begin{aligned}

4x - y =& 4
&& \text{Given equation}
\\
4x - 0 =& 4
&& \text{To find the $x$-intercepts, we let $y=0$ and solve for $x$}
\\
x =& 1
&& \text{Divide each side by $4$}

\end{aligned}
\end{equation}
$


The $x$-intercept is $1$.


$y$-intercepts


$
\begin{equation}
\begin{aligned}

4x - y =& 4
&& \text{Given equation}
\\
4(0) - y =& 4
&& \text{To find the $y$-intercepts, we let $x=0$ and solve for $y$}
\\
y =& -4
&& \text{Divide each side by $-1$}

\end{aligned}
\end{equation}
$


The $y$-intercept is $-4$.

Thus, the points are $(1,0)$ and $(0,-4)$.

Using the two points in slope formula


$
\begin{equation}
\begin{aligned}

m = \frac{y_2 - y_1}{x_2 - x_1} =& \frac{-4-0}{0-1}
&& \text{Substitute } (x_1, y_1) = (1,0) \text{ and } (x_2, y_2) = (0,-4)
\\
\\
=& \frac{-4}{-1}
&& \text{Simplify}
\\
\\
=& 4


\end{aligned}
\end{equation}
$