Question

What are the intercepts of the line `y=9/2x - 4`?

Answer 1

The y-intercept for the given line is `(0,-4)`.

The x-intercept is `(8/9,0)` or `(0.889,0)`.

Explanation:

Find the intercepts:

`y=9/2x-4`

This is a linear equation in slope-intercept form:

`y=mx+b`,

where:

`m` is the slope `(9/2)` and `b` is the y-intercept `(-4)`.

Y-intercept: value of `y` when `x=0`.

By definition, the y-intercept for the given line is `(0,-4)`.

X-intercept: value of `x` when `y=0`.

Substitute `0` for `y` and solve for `x`.

`0=9/2x-4`

Add `4` to both sides.

`4=9/2x`

Multiply both sides by `2`.

`8=9x`

Divide both sides by `9`.

`8/9=x`

The x-intercept is `(8/9,0)` or `(0.889,0)`.

You can graph the given line by plotting the x- and y-intercepts and drawing a straight line through them.

graph{y=9/2x-4 [-9.77, 10.23, -7.61, 2.39]}