Question

How do you graph `y=5/2x-2` using intercepts?

Answer 1

We can find that the x-intercept is `(4/5, 0)` and the y-intercept is `(0, -2)`.

Drawing a straight line through these two points creates a graph of the function.

Explanation:

The x-intercept is the point at which the function meets the x-axis, which is the line `y=0`.

If we substitute `y=0` into the equation, we get:

`0=5/2x−2`

Rearranging,

`5/2x =2`

`5x = 4`

`x=4/5`

So one point on the line is the point `(4/5, 0)`.

The y-intercept, similarly, is the point at which the function meets the y-axis, which is the line `x=0`. Substituting `x=0` into the equation yields:

`y =5/2(0)-2`

`y=-2`

So the y-intercept is the point `(0, -2)`.

Simply drawing a line through these two points will create a graph of the function, using intercepts.