# Are y=2/3x-2 and y=3/2x+1 parallel to each other?

Jan 11, 2017

No, they are not parallel because they have different slopes.

See full explanation below.

#### Explanation:

Parallel lines have the same slope.

You can determine the slope of a line if it is in slope-intercept form, which both of these equations are.

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.

Equation 1) $y = \textcolor{red}{\frac{2}{3}} x - \textcolor{b l u e}{2}$

Equation 2) $y = \textcolor{red}{\frac{3}{2}} x + \textcolor{b l u e}{1}$

The slope of the first equation is $m = \textcolor{red}{\frac{2}{3}}$ and the slope of the second equation is $m = \textcolor{red}{\frac{3}{2}}$, They are not equal and therefore they are not parallel.