## College Algebra (11th Edition)

$y=-2x+1$
$\bf{\text{Solution Outline:}}$ Use the Point-Slope Form of linear equations to find the equation of the line with the following given characteristcs: \begin{array}{l}\require{cancel} \text{through } (4,-7) \text{ having slope } -2 .\end{array} Use the properties of equality to express the equation in the slope-intercept form. $\bf{\text{Solution Details:}}$ Using $y-y_1=m(x-x_1)$ or the Point-Slope Form of linear equations, the equation of the line with the given conditions, \begin{array}{l}\require{cancel} y_1=-7 ,\\x_1=4 ,\\m=-2 ,\end{array} is \begin{array}{l}\require{cancel} y-(-7)=-2(x-4) \\\\ y+7=-2(x-4) .\end{array} Using the properties of equality, in the form $y=mx+b$ or the Slope-Intercept Form, the equation above is equivalent to \begin{array}{l}\require{cancel} y+7=-2(x)-2(-4) \\\\ y+7=-2x+8 \\\\ y=-2x+8-7 \\\\ y=-2x+1 .\end{array}