# How do you write an equation of a line going through (4,-1), (6,-7)?

Sep 25, 2016

$y = - 3 x + 11$

#### Explanation:

The equation of a line in $\textcolor{b l u e}{\text{point-slope form}}$ is

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y - {y}_{1} = m \left(x - {x}_{1}\right)} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and $\left({x}_{1} , {y}_{1}\right) \text{ a point on the line}$

To calculate m, use the $\textcolor{b l u e}{\text{gradient formula}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

The 2 points here are (4 ,-1) and (6 ,-7)

let $\left({x}_{1} , {y}_{1}\right) = \left(4 , - 1\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(6 , - 7\right)$

$\Rightarrow m = \frac{- 7 - \left(- 1\right)}{6 - 4} = \frac{- 6}{2} = - 3$

Use either of the 2 points for $\left({x}_{1} , {y}_{1}\right)$

We now have $m = - 3 \text{ and } \left({x}_{1} , {y}_{1}\right) = \left(4 , - 1\right)$

Substitute these values into the point-slope equation.

$y - \left(- 1\right) = - 3 \left(x - 4\right) \Rightarrow y + 1 = - 3 x + 12$

$\Rightarrow y = - 3 x + 11 \text{ is the equation of the line}$