Question

How do you write `2x-3y= 15` in slope-intercept form and graph it?

Answer 1

`y=2/3x-5`

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=15" into this form"`

subtract 2x from both sides.

`cancel(2x)cancel(-2x)-3y=-2x+15`

`rArr-3y=-2x+15`

divide ALL terms on both sides by - 3

`(cancel(-3) y)/cancel(-3)=(-2)/(-3)x+15/(-3)`

`rArry=2/3x-5larrcolor(red)" in slope-intercept form"`

The y-intercept is - 5`larrcolor(red)" 1 point on the graph"`

`"choose " x=3" and find y"`

`x=3toy=(2/3xx3)-5=2-5=-3`

`rArr(3,-3)larrcolor(red)" is a point on the graph"`

Plot the 2 points and draw a straight line through them and you have the graph.
graph{2/3x-5 [-10, 10, -5, 5]}