Question

How do you write an equation of a line with (4,0) and slope 1/3?

Answer 1

There are several ways to write an equation of the line with (4,0) and slope `1/3`.

1. Use Point-Slope form
2. Use Slope-Intercept form

First, Point-Slope form : `y - y_1=m(x-x_1)` where m is your slope, and the ordered pair you are given is `(x_1,y_1)`.
So write: `y - 0 = 1/3(x-4)`.
Simplify if you wish: `y = 1/3x-4/3`.

Or, Slope-Intercept form : y = mx + b, where m is your slope, and b is the y-intercept (not given).
So, write: `y = 1/3x+b`
Then, use your ordered pair to substitute in for x and y, and solve for b: `0 = (1/3)(4)+b`
`0 = 4/3+b` (subtract `4/3` from both sides)
`(-4)/3=b` and replace into the original form: `y = 1/3x-4/3`