Question

How do you find the slope that is perpendicular to the line `3x + 2y = -6`?

Answer 1

`"perpendicular slope "=2/3`

Explanation:

The equation of a line in `color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b, the y-intercept.

`"Rearrange " 3x+2y=-6" into this form"`

subtract 3x from both sides.

`cancel(3x)cancel(-3x)+2y=-3x-6`

`rArr2y=-3x-6`

divide both sides by 2

`(cancel(2) y)/cancel(2)=-3/2x-2`

`rArry=-3/2x-2larr" in slope-intercept form"`

`rArr"slope "=-3/2`

The slope perpendicular to this is the `color(blue)"negative reciprocal"` of m

`rArrm_("perpendicular")=-1/(-3/2)=2/3`