Question

How do you find the x and y intercept of `3x − 5y = −10`?

Answer 1

Isolate for each variable by subbing in `0` for the other. In this case, we get `(-10/3, 0)` as the `x`-intercept, and `(0, 2)` as the `y`-intercept.

Explanation:

To find the zeros, all we have to do is sub in one variable as `0` and isolate for the other.

Solving for `x`-intercept

This happens when the `y`-value is `0`, thus we sub in `0` as the `y`-value.

`3x - 5y = -10`

`3x - 5(0) = -10`

Now we solve for `x`.

`3x - 0 = -10`

`3x = -10`

`x = -10/3`

The `x`-intercept is `(-10/3, 0)`.

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Solving for `y`-intercept

This happens when the `x`-value is `0`, thus we sub in `0` as the `x`-value.

`3x - 5y = -10`

`3(0) - 5y= -10`

Now we solve for `y`.

`-5y= -10`

`y = (-10)/-5`

`y = 2`

The `y`-intercept is `(0, 2)`.

We can graph the equation to check our work.

graph{3x - 5y = -10 [-10, 10, -5, 5]}

As we can see, our intercepts are correct.

Hope this helps :)