Question

How do you find the slope and intercept of `-3x + 2y = 8`?

Answer 1

To find the slope and y-intercept of this line convert it to the slope-intercept form. See full explanation below.

Explanation:

To find the slope and y-intercept of this line convert it to the slope-intercept form.

The slope-intercept form of a linear equation is:

`y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b` is the y-intercept value.

We can solve this equation for `y` to get it into this format.

`-3x + 2y = 8`

`-3x + color(red)(3x) + 2y = color(red)(3x) + 8`

`0 + 2y = 3x + 8`

`2y = 3x + 8`

`(2y)/color(red)(2) = (3x + 8)/color(red)(2)`

`(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = (3x)/color(red)(2) + 8 /color(red)(2)`

`y = 3/2x + 4`

or

`y = color(red)(3/2)x + color(blue)(4)`

So the slope is `m = color(red)(3/2)`

And the y-intercept is `b = color(blue)(4)`