Question

How do you calculate the slope, x intercept, and y intercept of the following equation: `3x+6y = 9`?

Answer 1

The slope is `-1/2`.
The y-intercept is `3/2`.
The x-intercept is `3`.

Explanation:

Get the equation into slope-intercept form `y=mx+b` by solving for `y`. In the equation `y=mx+b`, `m` is the slope, and `b` is the y-intercept.

`6y=-3x+9`

Divide both sides by `6`.

`y=-3/6x+9/6` =

`y=-1/2x+3/2`

The slope is `-1/2` and the y-intercept is `3/2`.

To find the x-intercept, set `y` to zero, and solve for `x`.

`0=-1/2x+3/2`

Subtract `3/2` from both sides.

`-3/2=-1/2x`

Multiply both sides times `2`.

`-3=-x`

Multiply both sides times `-1`.

`3=x`

The x-intercept is `3`.

graph{3x+6y=9 [-10, 10, -5, 5]}