Question

How do you find the x and y intercept of `0.2x+3.2y=12.8`?

Answer 1

`x` intercept: `(64,0)`
`y` intercept: `(0,4)`

Explanation:

The axis intercepts are, as the name suggests, points on the given axis. So, the `x` intercept must be a point on the `x` axis, and the `y` intercept must be a point on the `y` axis.

By definition, a point lays on the `x` axis if its `y` coordinate equals zero, and vice versa. Let's use these conditions to find the results:

• For the `x` intercept, we need to set `y=0`:

`0.2x+3.2y=12.8 \to 0.2x+3.2(0)=12.8\implies 0.2x=12.8`

From here, we can easily solve for `x`:

`x=12.8/0.2 = 64`

And since we already knew that `y=0`, if `x=64` our point will be `(64,0)`

• For the `y` intercept, we do exactly the opposite: we know that our point will be of the form `(0,y)`, and we need to find `y`, setting `x=0`: after cancelling the `x` coefficient, the equation becomes

`3.2y = 12.8 \implies y=12.8/3.2 = 4`