# How do you write an equation of a line given (2,0) and (4,-6)?

May 3, 2017

$y = - 3 x + 6$

#### Explanation:

$\text{the equation of a line in "color(blue)"slope-intercept form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where m represents the slope and b, the y-intercept}$

$\text{to calculate the slope use the "color(blue)"gradient formula}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where " (x_1,y_1),(x_2,y_2)" are 2 coordinate points}$

$\text{the 2 points here are " (2,0)" and } \left(4 , - 6\right)$

$\text{let " (x_1,y_1)=(2,0)" and } \left({x}_{2} , {y}_{2}\right) = \left(4 , - 6\right)$

$\Rightarrow m = \frac{- 6 - 0}{4 - 2} = \frac{- 6}{2} = - 3$

$\Rightarrow y = - 3 x + b$

$\text{to find b, use either of the 2 given points}$

$\text{using " (2,0)" substitute into equation to find b}$

$\Rightarrow 0 = \left(- 3 \times 2\right) + b \Rightarrow b = 6$

$\Rightarrow y = - 3 x + 6 \leftarrow \textcolor{red}{\text{ is equation of line}}$