# How do you find the equation of the line passing through the points (4, 2) and (3, -4)?

Dec 13, 2016

$y - 4 = 6 \left(x - 2\right)$ or $y = 6 x - 8$

#### Explanation:

First, we need to find the slope of the equation. The formula for the slope of a linear equation is:

$\textcolor{red}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}}$ where $\textcolor{red}{m}$ is the slope and the two points are: $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ and $\textcolor{red}{\left(\left({x}_{2} , {y}_{2}\right)\right)}$

Substituting our points gives the slope as:

$m = \frac{- 4 - 2}{3 - 4}$

$m = \frac{- 6}{- 1}$

$m = 6$

We can now use the point-slope formula to find the equation of the line. The point-slope formula states:

$\textcolor{red}{\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)}$ where $m$ is the slope and #(x_1, y_1) is a given point on the line.

Substituting the information we have gives:

$y - 4 = 6 \left(x - 2\right)$

or, converting to standard form:

$y - 4 = 6 x - 12$

$y - 4 + 4 = 6 x - 12 + 4$

$y - 0 = 6 x - 8$

$y = 6 x - 8$