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

Apr 7, 2015

There are several ways to write an equation of the line with (4,0) and slope $\frac{1}{3}$.

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

First, Point-Slope form : $y - {y}_{1} = m \left(x - {x}_{1}\right)$ where m is your slope, and the ordered pair you are given is $\left({x}_{1} , {y}_{1}\right)$.
So write: $y - 0 = \frac{1}{3} \left(x - 4\right)$.
Simplify if you wish: $y = \frac{1}{3} x - \frac{4}{3}$.

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