# How do you find the slope perpendicular to 1/3x + 2/3y = 2?

Jun 13, 2018

$\text{perpendicular slope } = 2$

#### Explanation:

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

•color(white)(x)y=mx+b

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

$\text{rearrange "1/3x+2/3y=2" into this form}$

$\text{multiply all terms by 3}$

$x + 2 y = 6$

$\text{subtract "x" from both sides and divide by 2}$

$y = - \frac{1}{2} x + 3 \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope } = - \frac{1}{2}$

$\text{the slope of perpendicular to it is}$

•color(white)(x)m_(color(red)"perpendicular")=-1/m=-1/(-1/2)=2