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 $(-4,-3)$.