# How do you write an equation of a line passing through (4, -2), perpendicular to y = 4x + 2?

Sep 5, 2017

See a solution process below:

#### Explanation:

The equation in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

$y = \textcolor{red}{4} x + \textcolor{b l u e}{2}$

The slope of this line is: $\textcolor{red}{m = 4}$

Let's call the slope of the line perpendicular to the line in the problem: ${m}_{p}$

The formula for the slope of a perpendicular line is: ${m}_{p} = - \frac{1}{m}$

Substituting gives the slope of the line we are looking for as:

${m}_{p} = - \frac{1}{4}$

We can substitute this into the slope-intercept formula giving:

$y = \textcolor{red}{- \frac{1}{4}} x + \textcolor{b l u e}{b}$

We can now substitute the values from the point in the problem for $x$ and $y$ in the formula and solve for $\textcolor{b l u e}{b}$ giving:

$- 2 = \left(\textcolor{red}{- \frac{1}{4}} \times 4\right) + \textcolor{b l u e}{b}$

$- 2 = \textcolor{red}{- 1} + \textcolor{b l u e}{b}$

$1 - 2 = 1 \textcolor{red}{- 1} + \textcolor{b l u e}{b}$

$- 1 = 0 + \textcolor{b l u e}{b}$

$- 1 = \textcolor{b l u e}{b}$

Substituting this back into the formula gives:

$y = \textcolor{red}{- \frac{1}{4}} x + \textcolor{b l u e}{- 1}$

$y = \textcolor{red}{- \frac{1}{4}} x - \textcolor{b l u e}{1}$