# How do you find the slope of the line parallel to and perpendicular to y+3=3x+2?

Jun 7, 2018

$m ' = 3$

$m ' = - \frac{1}{3}$

#### Explanation:

$y + 3 = 3 x + 2$

convert to slope intercept form $y = m x + b$

$y = 3 x - 1$

So slope of this line $m = 3$

Slope of a parallel line: $m ' = m$:

$m ' = 3$

Slope of a perpendicular line $m ' = - \frac{1}{m}$

$m ' = - \frac{1}{3}$

Jun 7, 2018

$3 \text{ and } - \frac{1}{3}$

#### Explanation:

• " parallel lines have equal slopes"

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$y + 3 = 3 x + 2 \text{ can be written as}$

$y = 3 x - 1 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope m "=3" and y-intercept } = - 1$

$\text{thus a line parallel to it has slope } = 3$

$\text{given a line with slope m then the slope of a line}$
$\text{perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m

$\Rightarrow {m}_{\text{perpendicular}} = - \frac{1}{3}$

$\text{thus a line perpendicular to it has slope } = - \frac{1}{3}$

Jun 7, 2018

Parallel slope: $3$
Perpendicular slope: $- \frac{1}{3}$

#### Explanation:

I'm assuming that you're actually asking two questions, so let's split them up: in general, given two lines with slopes ${m}_{1}$ and ${m}_{2}$, the lines are parallel if ${m}_{1} = {m}_{2}$, while their are perpendicular if ${m}_{1} = - \frac{1}{m} _ 2$

To find the slope of a line from its equation, you can write it in the form $y = m x + b$. The slope will be the $x$ coefficient, i.e. $m$.

In your case, you only need to subtract $3$ from both sides to get

$y = 3 x - 1$

so the slope is $3$.

This means that any line parallel to the given line will have slope $3$ as well, while all the perpendicular lines will have slope $- \frac{1}{3}$