Question

What is the `y`-intercept of the line `2x-3y = -6`?

Answer 1

The y-intercept is the point on the y-axis where the line crosses. The y-axis is the line `x=0`, so substitute in `0` for `x` and solve. The y-intercept is `y=2`.

Explanation:

The y-axis is the line `x=0`. Substitute in `0` for `x` in the equation to find the y-intercept:

`2x-3y=-6`

`2(0)-3y=-6`

`-3y=-6`

`y=(-6)/-3 = 2`

The y-intercept is simply `y=2`.

Answer 2

The answer is, in coordinate-pair format: `(0, 2)`

Explanation:

The `y`-intercept is the value of `y` when `x=0`.

That means to solve this we should replace `x` with `0` and solve for `y`.

Now the equation looks lie this `2(0)-3y=-6`.
From here, I would solve `2x*0`, which is `0`. The equation is now `-3y=-6`, and from here I would divide both sides by `-3`. The updated version of the equation is `y=-6/-3`,or `y=2`.

We can also graph the equation and check where the `y`-intercept is.

graph{-6=2x-3y}
In this case, it is at (0, 2), which is what we found. We were right!