Question

How do you graph and find the `x` and `y` intercepts of `y = -1/2x + 6`?

Answer 1

X intercept: `X = 12`

Y intercept: `Y = 6`

Explanation:

Here's the graph for your function.
Read further below for solution steps.
graph{-1/2x+6 [-10, 10, -5, 5]}
Starting with the easiest one to deduce, the Y intercept is simply the point on the graph where the function intersects with the Y axis, at `x = 0`.

So just substitute `x` with `0`, solve, and you'll have your `y` value.

`y=-1/2(color(red)(0))+6`
`y=6`

The X intercept is the point where the function intersects with the X axis, at `y = 0`.

In this case, we wish to get the `x` value, so we first need to isolate `x` to get the answer:

`color(red)(0)-6=-1/2x+6-6`

`{-6}/{-1/2}={-1/2x}/{-1/2}`

`12=x`

`therefore x=12`

You can now compare to the graph, and see that the results are exactly as those that were calculated.