# How do you write the equation of a line given (6,1) (-3,-2)?

May 28, 2016

$y = \frac{1}{3} x - 1$

#### Explanation:

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

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where m represents the slope and b, the y-intercept.

To obtain the equation ,we require to find m and b.

m can be calculated using 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 $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 points}$

let $\left({x}_{1} , {y}_{1}\right) = \left(6 , 1\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 3 , - 2\right)$

$\Rightarrow m = \frac{- 2 - 1}{- 3 - 6} = \frac{- 3}{- 9} = \frac{1}{3}$

Partial equation is $y = \frac{1}{3} x + b$

To find b , substitute one of the 2 given points into the partial equation, say (-3 ,-2)

x = -3 , y = -2 gives.

-2=(1/3xx-3)+b→-2=-1+b→b=-1

$\Rightarrow y = \frac{1}{3} x - 1 \text{ is the equation of the line}$
graph{1/3x-1 [-10, 10, -5, 5]}