# How do you write the equation in slope intercept form given (5, 1), (0, -6)?

Jul 24, 2016

$y = \frac{7}{5} x - 6$

#### 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.

To calculate 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 points here are (5 ,1) and (0 ,-6)

let $\left({x}_{1} , {y}_{1}\right) = \left(5 , 1\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(0 , - 6\right)$

$\Rightarrow m = \frac{- 6 - 1}{0 - 5} = \frac{- 7}{- 5} = \frac{7}{5}$

We are given the point (0 ,-6) which is the point where the line crosses the y-axis, hence the y-intercept b = -6

$\Rightarrow y = \frac{7}{5} x - 6 \text{ is the equation in slope-intercept form.}$