# What is the equation of the line with slope  m= 4/25  that passes through  (12/5 29/10) ?

Dec 30, 2015

In general form:

$20 x - 125 y + 629 = 0$

#### Explanation:

The equation of a line of slope $m$ passing through a point $\left({x}_{1} , {y}_{1}\right)$ can be written in point slope form as:

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

So in our example, we can write:

$\textcolor{b l u e}{y - \frac{29}{10} = \frac{4}{25} \left(x - \frac{12}{5}\right)}$

Multiplying this out and adding $\frac{29}{10}$ to both sides we get:

$y = \frac{4}{25} x - \frac{48}{125} + \frac{29}{10}$

$= \frac{4}{25} x - \frac{96}{250} + \frac{725}{250}$

$= \frac{4}{25} x + \frac{629}{125}$

The equation:

$\textcolor{b l u e}{y = \frac{4}{25} x + \frac{629}{125}}$

is in slope intercept form.

If we multiply both sides by $125$ then we get:

$125 y = 20 x + 629$

Subtract $125 y$ from both sides and transpose to get:

$\textcolor{b l u e}{20 x - 125 y + 629 = 0}$

This is the general form of the equation of a line, which can cope with lines of any slope.