# A line has the equation 2y=-3x+1, how do you find an equation of a line parallel to this line that has a y intercept of -2?

Jan 10, 2017

See the process for solving this problem below in the Explanation:

#### Explanation:

First, we need to put the line from the problem in the slope-intercept form by solving for $y$:

$\frac{2 y}{\textcolor{red}{2}} = \frac{- 3 x + 1}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} y}{\cancel{\textcolor{red}{2}}} = - \frac{3}{2} x + \frac{1}{2}$

$y = - \frac{3}{2} x + \frac{1}{2}$

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 color(blue)(b is the y-intercept value.

So we know the slope of the line from the question is $- \frac{3}{2}$

And, a parallel line by definition has the same slope so the slope of the line we are looking for also has a slope of $- \frac{3}{2}$

And because we know the $y$ intercept, $- 2$, we can substitute both these values into the slope-intercept formula to find the equation we are looking for:

$y = \textcolor{red}{- \frac{3}{2}} x + \textcolor{b l u e}{- 2}$

$y = \textcolor{red}{- \frac{3}{2}} x - \textcolor{b l u e}{2}$