Precalculus, Chapter 1, 1.3, Section 1.3, Problem 54

Determine an equation for the line with $x$-intercept $-4$ and $y$-intercept $4$. Express your answer using the general form or the slope intercept form of the equation of a line, which ever you prefer.

Using the intercept form, $\displaystyle \frac{x}{a} + \frac{y}{b} = 1$, where $a$ is the $x$-intercept and $b$ is the $y$-intercept.


$
\begin{equation}
\begin{aligned}

\frac{x}{-4} + \frac{y}{4} =& 1
&& \text{Substitute } a = -4 \text{ and } b = 4
\\
\\
\frac{1}{4} (-x + y) =& 1
&& \text{Factor out } \frac{1}{4}
\\
\\
-x+y =& 4
&& \text{General Form}
\\
\text{or} &
&&
\\
y =& x + 4
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$