Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 122

a. Prove that the equation $y+3 = 2(x+4)$ is a linear equation by writing it in the form $y = mx + b$.


$
\begin{equation}
\begin{aligned}

y+3 =& 2(x + 4)
&& \text{Given equation}
\\
y+3 =& 2x + 8
&& \text{Apply Distributive Property}
\\
y + 3 - 3 =& 2x+8 - 3
&& \text{Subtract } 3
\\
y =& 2x+5
&&

\end{aligned}
\end{equation}
$


b. Determine the ordered-pair solution that corresponds to $x = -4$.

Using the equation in part a.


$
\begin{equation}
\begin{aligned}

y =& 2(-4)+5
&& \text{Substitute } x = -4
\\
y =& -8+5
&& \text{Simplify}
\\
y =& -3
&&

\end{aligned}
\end{equation}
$


The ordered-pair is $(-4,-3)$.