# How do you write an equation in slope-intercept form of the line that passes through the points (-2,-1) and (4,2)?

Dec 3, 2016

$y = \frac{1}{2} x$

#### Explanation:

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

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = m x + b} \textcolor{w h i t e}{\frac{2}{2}} |}}}$
where m represents the slope and b, the y-intercept.

We have to find m and b.

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

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

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

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

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

We can write the partial equation as $y = \frac{1}{2} x + b$

To find b, substitute either of the 2 given points into the
partial equation

Choosing the point (4 ,2) that is x = 4 and y = 2

$\Rightarrow 2 = \left(\frac{1}{2} \times 4\right) + b$

$\text{Thus } 2 = 2 + b \Rightarrow b = 0$

$\Rightarrow y = \frac{1}{2} x \text{ is the equation of the line}$
graph{1/2x [-10, 10, -5, 5]}