Intermediate Algebra, Chapter 3, Test, Section Test, Problem 12

Determine an equation of the line "through $(-2,3)$ and $(6,-1)$", and write it in the following form:

a.) Slope-intercept form

Using the Slope Formula

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - 3}{6 - (-2)} = - \frac{4}{8} = - \frac{1}{2}$

The slope is $\displaystyle - \frac{1}{2}$.

Using Point Slope Form


$\begin{equation} \begin{aligned} y - y_1 =& m(x - x_1) && \text{Point Slope Form} \\ \\ y - 3 =& - \frac{1}{2} [x - (-2)] && \text{Substitute } x = -2, y = 3 \text{ and } m = - \frac{1}{2} \\ \\ y - 3 =& - \frac{1}{2}x - 1 && \text{Distributive Property} \\ \\ y =& - \frac{1}{2}x + 2 && \text{Slope Intercept Form} \end{aligned} \end{equation}$



b.) Standard Form


$\begin{equation} \begin{aligned} & y = - \frac{1}{2}x + 2 && \text{Slope Intercept Form} \\ \\ & \frac{1}{2}x + y = 2 && \text{Standard Form} \\ & \text{or} && \\ & x + 2y = 4 && \end{aligned} \end{equation}$