## Intermediate Algebra (12th Edition)

$\text{Slope-Intercept Form: } y=-4x+15 \\\text{Standard Form: } 4x+y=15$
Use the Point-Slope Form of linear equations to find the equation of the line passing through $( 4,-1 )$ and with $m= -4 .$ 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 is \begin{array}{l}\require{cancel} y-(-1)=-4(x-4) \\\\ y+1=-4(x-4) .\end{array} Using $y=mx+b$ or the Slope-Intercept Form of linear equations, the equation above is equivalent to \begin{array}{l}\require{cancel} y+1=-4x+16 \\\\ y=-4x+16-1 \\\\ y=-4x+15 .\end{array} Using $Ax+By=C$ or the Standard Form of linear equations, the equation above is equivalent to \begin{array}{l}\require{cancel} 4x+y=15 .\end{array} Hence, the equation of the line is \begin{array}{l}\require{cancel} \text{Slope-Intercept Form: } y=-4x+15 \\\text{Standard Form: } 4x+y=15 .\end{array}