# What is the equation of a line passing through the point (a, b) and having a a slope of b?

Nov 14, 2016

$x - \frac{1}{b} y = a - 1$

#### Explanation:

In general the slope-point form of a line with slope $\textcolor{g r e e n}{m}$ through a point $\left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$ is
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{b} = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{a}\right)$

In this case, we are given a slope of $\textcolor{g r e e n}{b}$
So our equation becomes
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{b} = \textcolor{g r e e n}{b} \left(x - \textcolor{red}{a}\right)$

Dividing through by $b$
$\textcolor{w h i t e}{\text{XXX}} \frac{1}{b} y - 1 = x - a$

Then converting to standard form:
$\textcolor{w h i t e}{\text{XXX}} x - \frac{1}{b} y = a - 1$