How do you find an equation of the line passing through the given points (-4,-7) and (-8, -8)?

Oct 24, 2016

$y = \frac{1}{4} x - 6$

Explanation:

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

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

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

here the 2 points are $\left(- 4 , - 7\right) \mathmr{and} \left(- 8 , - 8\right)$

let $\left({x}_{1} , {y}_{1}\right) = \left(- 4 , - 7\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 8 , - 8\right)$

$\Rightarrow m = \frac{- 8 - \left(- 7\right)}{- 8 - \left(- 4\right)} = \frac{- 1}{- 4} = \frac{1}{4}$

We can now write the partial equation as.

$y = \frac{1}{4} x + b$

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

Using (-4 ,-7). That is $x = - 4 \mathmr{and} y = - 7$

$\left(\frac{1}{4} \times - 4\right) + b = - 7 \Rightarrow - 1 + b = - 7 \Rightarrow b = - 6$

$\Rightarrow y = \frac{1}{4} x - 6 \text{ is the equation}$