Question

Determine the slope of this line: -x-3y=-6

Answer 1

The slope of this line is -1/3

Answer 2

`-(1)/(3)`

Explanation:

In order to find slope, we need to put this equation into slope-intercept form as shown below.

• 
  `y=mx+b`
• In this case
  `m` is slope, and
  `b` is the line's y-intercept.

In order to get our equation into this form, we need to isolate
`y` on the left side of the equation. Here's how we do it...

`-x-3y=-6`

• First, let's add
  `x` to both sides of this equation to get rid of the
  `-x` on the left side.

`-3y=-6+x` ⇒
`-3y=x-6`

• Now, let's divide both sides by
  `-3`. This will isolate
  `y` on the left side and get our equation into slope-intercept form.

`y=(x)/(-3)+(6)/(3)`

• All we need to do now is simplify. I'll show how I simplified
  `(x)/(3)` with more than 1 step to make things less confusing hopefully.

`y=(1x)/(-3)+2`

`y=(1)/(-3)((x)/(1))+2`

`y=-(1)/(3)x+2`

• Our final, simplified answer is shown above.

Now that our formula is in the same format as
`y=mx+b` we know that:

1. 
   `m=-(1)/(3)`
2. 
   `b=2`

Our formula has a slope of
`-(1)/(3)` and a y-intercept of
`2`.