## Precalculus (6th Edition) Blitzer

The slope-intercept form of line is$f\left( x \right)=-\frac{1}{4}x-6$
Consider the equation $4x-y-6=0$. Isolate y terms on one side. \begin{align} & 4x-y-6=0 \\ & -y=-4x+6 \end{align} Divide both sides of the equation by $-1$ to remove the negative sign. \begin{align} & -\frac{y}{-1}=\frac{-4x+6}{-1} \\ & y=4x-6 \end{align} Hence, the slope ${{m}_{1}}$ of the line $4x-y-6=0$ is ${{m}_{1}}=4$ and the y-intercept is $-6$. Now, let the slope of the line $f$ be ${{m}_{2}}$. So, \begin{align} & {{m}_{1}}\cdot {{m}_{2}}=-1 \\ & 4\cdot {{m}_{2}}=-1 \\ & {{m}_{2}}=-1\left( \frac{1}{4} \right) \\ & {{m}_{2}}=-\frac{1}{4} \end{align} The y-intercept is equal -- that is, $\left( 0,-6 \right)$. Now, the equation of $f$ having point $\left( 0,-6 \right)$ and slope $-\frac{1}{4}$ is: \begin{align} & f\left( x \right)=mx+b \\ & =-\frac{1}{4}\left( x \right)+\left( -6 \right) \\ & =-\frac{1}{4}x-6 \end{align} Hence, the equation of the line in slope intercept form of the line which is perpendicular to the line $4x-y-6=0$ and has the same y intercept is $f\left( x \right)=-\frac{1}{4}x-6$.