Question

What is the slope-intercept form of `10x - 5y = -2`?

Answer 1

`y = 2x + 2/5`

Explanation:

`10x - 5y = -2`

We know that slope-intercept form is:

To make the equation in this form, find `y` by itself.

Subtract `color(blue)(10x)` from both sides:

`10x - 5y quadcolor(blue)(-quad10x) = -2 quadcolor(blue)(-quad10x)`

`-5y = -2 - 10x`

Divide both sides by `color(blue)(-5)`:
`(-5y)/color(blue)(-5) = (-2-10x)/color(blue)(-5)`

`y = 2/5 + 2x`

`y = 2x + 2/5`

As you can see, this matches the slope-intercept form in the image.

Hope this helps!

Answer 2

`y=2x+2/5`

Explanation:

Recall the equation of a line in slope-intercept form

`y=mx+b`, with slope `m` and a `y`-intercept of `b`.

We essentially just want a `y` on the left. Let's start by subtracting `10x` from both sides to get

`-5y=-10x-2`

Lastly, we can divide both sides by `-5` to get

`y=2x+2/5`

Now, our equation is in slope-intercept form, with slope `2` and a `y`-intercept of `2/5`.

Hope this helps!