Question

How do you write equation of a line goes through (3,1), with slope of m=1/3?

Answer 1

Use point-slope form `y-y_1=m (x-x_1)`

Explanation:

For this equation that would turn into `y-1=1/3 (x-3)` then solve which should look like `y=1/3x`

Answer 2

`y=1/3 x`

Explanation:

You know the equation of a line: `y=mx+b`

You are given the point `(3, 1)`. That is the same as saying that `x=3` and `y=1`.

You are given the slope, `m=1/3`. That means that after you "rise" one point on the `y`-axis, you must "run" 3 points on the `x`-axis to get to another point on that line.

Plugging the `x=3`, `y=1`, and `m=1/3` into the equation of a line, you get the following:

`y=mx+b` becomes `1 = 3 * 1/3 + b`. The only variable you don't know yet is `b`. So solve for `b`.

`1 = 3 * 1/3 + b`
`1 = 1 + b`
`b=0`

The final step is to plug just the slope, `m` (previously given), and the `y`-intercept, `b` (which you just found), into the formula `y=mx+b`, giving you:

`y=1/3*x + 0` or simply `y=1/3*x`