Question

How do you determine the slope and y-intercept of the graph of 12+3y= -2x?

Answer 1

slope `=-2/3`
y-intercept = -4

Explanation:

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

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

The advantage to having the line in this form is that m and b may be extracted 'easily ' from it.

`12+3y=-2x" can be written in this form"`

subtract 12 from both sides.

`cancel(12)cancel(-12)+3y=-2x-12`

`rArr3y=-2x-12`

divide both sides by 3.

`(cancel(3) y)/cancel(3)=-2/3 x-12/3`

`rArry=-2/3x-4larr" now in form y=mx+b"`

`rArr"slope" =-2/3" and y-intercept" =-4`
graph{-2/3x-4 [-10, 10, -5, 5]}