Question

Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of each equation.

$\left(-3,6\right)$,$y=\frac{1}{4}x+2$

Short answer

The required equation is represented by $y=-4x-6$.

Step-by-step solution

Step 1. Determine the slope of provided equation.

Take the help of the standard form $y=mx+c$ in which the representation of the slope is m so compare this equation with the provided equation.

$m=\frac{1}{4}$

Step 2. Determine the required equation.

Take the help of obtained standard form represented by $y-y_1=m\left(x-x_1\right)$in which the required values can be filled by using the reverse of obtained slope that is $-4$because both the lines are having a perpendicular relation so their slope will be reverse of each other and take provided point as it is in the form of $\left(x_1,y_1\right)$.

$$\begin{gathered} y-6=\left(-4\right)\left(x-\left(-3\right)\right) \\ y-6=-4x-12 \\ y=-4x-12+6 \\ y=-4x-6 \end{gathered}$$

Step 3. Write the conclusion.`

The obtained equation is$y=-4x-6$ so it is the required equation.