Question

Question #af9fd

Answer 1

`"slope "=-2/3" and y-intercept "=2`

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

subtract 2x from both sides.

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

`rArr3y=-2x+6`

divide ALL terms on both sides by 3

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

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

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