Question

How do you graph `20x + 80y = 0`?

Answer 1

The equation in slope intercept form is `y=-1/4x`, where the slope, `m` is `-1/4` and the y-intercept, `b` is `0`.

Explanation:

`20x+80y=0` is the standard form for a linear equation. Solve for `y` in order to convert the equation to slope-intercept form, `y=mx+b`, where `m` is the slope and `b` is the y-intercept.

`20x+80y=0`

Subtract `20x` from both sides.

`80y=-20x`

Divide both sides by `80`.

`y=(-20x)/80=`

`y=-1/4x`

The slope, `m` is `-1/4` and the y-intercept, `b` is `0`.

Graphing the equation

`y=-1/4x`

Substitute `0` for `x`.

`y=-1/4(0)=0`

This gives us a point at the origin, `0,0`.

To use the slope to determine other points, you can use the slope of `-1/4`. Starting at the origin, go up `1` and over `-4`, keeping going as far as you want. You can also start at the origin and go down `1` and over `4`, keeping going as far as you want. You really only need two points to graph a straight line.

You can also substitute values for `x` into the equation and solve for `y`.

If `x=4,` `y=-1`

If `x=-4,` `y=1`

Below is how the graph of `y=-1/4x` would look.

graph{y=-1/4x [-10, 10, -5, 5]}