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.

$\left(1,4\right)$,$y=-2x+5$

Short answer

The required equation is represented by $y=\frac{1}{2}x+\frac{7}{2}$.

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.

$m=-2$

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 $\frac{1}{2}$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 $\left(x_1,y_1\right)$.

$$\begin{gathered} y-4=\frac{1}{2}\left(x-1\right) \\ y-4=\frac{1}{2}x-\frac{1}{2} \\ y=\frac{1}{2}x-\frac{1}{2}+4 \\ y=\frac{1}{2}x+\frac{7}{2} \end{gathered}$$

Step 3. Write the conclusion.

The obtained equation is$y=\frac{1}{2}x+\frac{7}{2}$ so it is the required equation.