# How do you write the equation of a line through (0,3) and (-2,5)?

Nov 16, 2016

$y = - x + 3$

#### 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 require 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 $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 points on the line}$

The 2 points here are (0 ,3) and (-2 ,5)

let $\left({x}_{1} , {y}_{1}\right) = \left(0 , 3\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 2 , 5\right)$

$\Rightarrow m = \frac{5 - 3}{- 2 - 0} = \frac{2}{- 2} = - 1$

One of the points here is (0 ,3). That is where the line crosses the y-axis.
Hence the value of b is 3

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