Question

How do you write `3x - 2y= 5` into slope intercept form?

Answer 1

`y = 3/2x - 5/2`

Explanation:

For a general line `y`, the equation of the line in slope-intercept form looks like this

`color(blue)(y = mx + b)" "`, where

`m` - the slope of the line;
`b` - the `y`-intercept.

So basically, all you have to do to write the equation for your line in sloper-intercept form is isolate `y` on one side of the equation.

Start by adding `-3x` to both sides to get

`-color(red)(cancel(color(black)(3x))) + color(red)(cancel(color(black)(3x))) - 2y = 5 - 3x`

`-2y = -3x + 5`

Now divide both sides of the equation by `-2` to get

`(color(red)(cancel(color(black)(-2))) * y)/color(red)(cancel(color(black)(-2))) = ((-3))/((-2))x + 5/((-2))`

`color(green)(y = 3/2x - 5/2)`