Question

How do you find the equation of a line with a slope of 2 and a y intercept of (0,0)?

Answer 1

Use slope-intercept form. See below.

Explanation:

Slope-intercept form is given by `y=mx+b`, where `m` is the slope of the line and `b` is the `y`-intercept of the line, or the value of `y` where the line crosses the `y`-axis.

Given that the slope of the line is `2`, we have `m=2`, and because the line crosses the `y`-axis at the point `(0,0)`, where `y=0` and `x-0`, we have:

`y=2x+0`

Or, equivalently, `y=2x`

If the point given were not the origin, you could use `y=mx+b` to find `b` by plugging the `x` and `y` value of the point in for `x` and `y` in the equation along with the given slope `m` and solving for `b`.

Given `m=2` and `(x,y)=(0,0)`:

`0=2(0)+b`

`=>0=b`

We would then put this value back into `y=mx+b` for `b`, along with the slope `m`, yielding the same answer as above: `y=2x`.