# How do you write an equation in standard form for a line through (1,2) with slope 4/5?

May 19, 2015

The formula for a line expressed in slope intercept form is:

$y = m x + c$

where $m$ is the slope and $c$ is the intercept.

We have been given $m = \frac{4}{5}$ and an example point with $x = 1$ and $y = 2$ which will satisfy this equation. Subtracting $m x$ from both sides we have:

$c = y - m x = 2 - \left(\frac{4}{5} \times 1\right) = 2 - \frac{4}{5} = \frac{10}{5} - \frac{4}{5} = \frac{6}{5}$

$y = \frac{4}{5} x + \frac{6}{5}$