# How do you write a slope-intercept equation for a line perpendicular to y=2x-4 that contains the point (-6, 2)?

Aug 23, 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.

For: $y = \textcolor{red}{2} x - \textcolor{b l u e}{4}$ the slope is:

$\textcolor{red}{m = 2}$

We can substitute this into the formula to give:

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

Into this we can substitute the values of the points in the problem for $x$ and $y$ in the formula and solve for $\textcolor{b l u e}{b}$ giving:

$2 = \left(\textcolor{red}{2} \times - 6\right) + \textcolor{b l u e}{b}$

$2 = - 12 + \textcolor{b l u e}{b}$

$\textcolor{red}{12} + 2 = \textcolor{red}{12} - 12 + \textcolor{b l u e}{b}$

$14 = 0 + \textcolor{b l u e}{b}$

$14 = \textcolor{b l u e}{b}$

$\textcolor{b l u e}{b} = 14$

We can now substitute the slope and the value for $\textcolor{b l u e}{b}$ into the formula to give the solution as:

$y = \textcolor{red}{2} x + \textcolor{b l u e}{14}$