Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 2

To find the equation of the line that contains the point whose coordinates are $(-4,1)$ and has slope $\displaystyle \frac{3}{2}$, first use the given point and slope to find the $y$-intercept of the line:


$\begin{equation} \begin{aligned} y =& mx + b && \text{Write the slope-intercept form of the equation of a line} \\ \\ 1 =& \frac{3}{2} (-4) + b && \text{Substitute $\underline{1}$ for } y, \underline{\frac{3}{2}} \text{ for $m$ and $\underline{-4}$ for $x$} \\ \\ 1 =& b && \text{Solve for } b \\ \\ \underline{\frac{-6}{7}} =& b \end{aligned} \end{equation}$


The $y$-intercept of the line through $(-4,1)$ that has slope $\displaystyle \frac{3}{2}$ is $(0, \underline{7})$.