Precalculus, Chapter 1, 1.3, Section 1.3, Problem 100

a. Determine the intercepts of the graph of the equation $-0.3x + 0.4y = 1.2$.

$x$-intercepts:


$
\begin{equation}
\begin{aligned}

-0.3x + 0.4y =& 1.2
&& \text{Given equation}
\\
-0.3x + 0.4(0) =& 1.2
&& \text{To find the $x$-intercept, we let $y = 0$ and solve for $x$}
\\
-0.3x =& 1.2
&&
\\
x =& -4
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(-4,0)$


$y$-intercepts:


$
\begin{equation}
\begin{aligned}

-0.3x + 0.4y =& 1.2
&& \text{Given equation}
\\
-0.3(0) + 0.4y =& 1.2
&& \text{To find the $y$-intercept, we let $x = 0$ and solve for $y$}
\\
0.4y =& 1.2
&&
\\
y =& 3
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,3)$


Graph the equation