# What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of 1/3?

Apr 1, 2017

$x - 3 y = 7$

#### Explanation:

The point-slope form for a line passing through $\left(x , y\right) = \left(\textcolor{red}{a} , \textcolor{b l u e}{b}\right)$ with a slope of $\textcolor{g r e e n}{m}$ is
$\textcolor{w h i t e}{\text{XXX}} y - \textcolor{b l u e}{b} = \textcolor{g r e e n}{m} \left(x - \textcolor{red}{a}\right)$ or some modified version of this

Given $\left(x , y\right) = \left(\textcolor{red}{1} , \textcolor{b l u e}{- 2}\right)$ and a slope of $\textcolor{g r e e n}{m}$ this becomes:
color(white)("XXX")y-(color(blue)(-2)))=color(green)(1/3)(x-color(red)1)
or
$\textcolor{w h i t e}{\text{XXX}} y + 2 = \frac{1}{3} \left(x - 1\right)$

Typically, you might want to convert this into "standard form": $A x + B y = C$ (often with the restrictions $A \ge 0$ and $G C F \left(A , B , C\right) = 1$).

$y + 2 = \frac{1}{3} \left(x - 1\right)$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 3 y + 6 = x - 1$

$\textcolor{w h i t e}{\text{XXX}} \Rightarrow 1 x - 3 y = 7$