Question

How do you write `x-2y-2=0` into slope intercept form?

Answer 1

`y = 1/2x - 1`

Explanation:

The equation of a line in slope-intercept form looks like this

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

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

In your case, you have all the terms on one side of the equation. This means that you can write the equation in slope-intercept form by moving the `y`-term to the other side of the equation, the dividing all the terms by `2`.

This will get you

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

`x - 2 = 2y`

`1/2x - 2/2 = (color(red)(cancel(color(black)(2))) * y)/color(red)(cancel(color(black)(2)))`

The slope-intercept form for your line will be

`color(green)(y = 1/2x - 1)`