Question

What is `12x-4y=-8` written in slope-intercept form?

Answer 1

See a solution process below:

Explanation:

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.

Solving this equation for `y` gives:

`12x - 4y = -8`

`-color(red)(12x) + 12x - 4y = -color(red)(12x) - 8`

`0 - 4y = -12x - 8`

`-4y = -12x - 8`

`(-4y)/color(red)(-4) = (-12x - 8)/color(red)(-4)`

`(color(red)(cancel(color(black)(-4)))y)/cancel(color(red)(-4)) = (-12x)/color(red)(-4) - 8/color(red)(-4)`

`y = 3x - (-2)`

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

Answer 2

`color(crimson)(y = 3 x + 2`

Slope = m = 3, y-intercept = c = 2#

Explanation:

Slope- intercept form of equation `y = m x + c`

`12x - 4y = -8`

`12x + 8 = 4y`

`y = (12/4)x + (8/2)`

`color(crimson)(y = 3 x + 2`

Slope = m = 3, y-intercept = c = 2#