# How do you write the standard form of a line given (3,-2) and (7,6)?

Jun 28, 2016

y = 2x - 8

#### 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.

We require to find m and b to obtain the equation.

To find 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 $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 points} .$

The 2 coordinate points here are (3 ,-2) and (7 ,6)

let $\left({x}_{1} , {y}_{1}\right) = \left(3 , - 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(7 , 6\right)$

$\Rightarrow m = \frac{6 - \left(- 2\right)}{7 - 3} = \frac{8}{4} = 2$

We now have a partial equation: y= 2x + b and to find b use either of the 2 given coordinate points.

Using (7 ,6) and substituting x = 7 , y = 6 into the partial equation.

$: 6 = \left(2 \times 7\right) + b \Rightarrow 14 + b = 6 \Rightarrow b = 6 - 14 = - 8$

$\Rightarrow y = 2 x - 8 \text{ is the equation}$