# How do you write the point-slope form of the equation given (4,0) and (0,4)?

Jun 9, 2018

$y - 0 = - 1 \left(x - 4\right)$

#### Explanation:

We have after the formula
$y - {y}_{0} = m \left(x - {x}_{0}\right)$
$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{4 - 0}{0 - 4} = - 1$

$y - 0 = - 1 \left(x - 4\right)$

Jun 9, 2018

$\left(y - 4\right) = - 1 \left(x - 0\right)$

#### Explanation:

Slope point formula

First you determine the slope:

$\left(\textcolor{b l u e}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right) = \left(4 , 0\right)$

$\left(\textcolor{red}{{x}_{2}} , \textcolor{red}{{y}_{2}}\right) = \left(0 , 4\right)$

$\textcolor{g r e e n}{m} = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

$\textcolor{g r e e n}{m} = \frac{\textcolor{red}{4} - \textcolor{b l u e}{0}}{\textcolor{red}{0} - \textcolor{b l u e}{4}} = - 1$

Now use the Point Slope form of a line:

$\left(y - \textcolor{b l u e}{{y}_{1}}\right) = \textcolor{g r e e n}{m} \left(x - \textcolor{b l u e}{{x}_{1}}\right)$

$\left(y - \textcolor{b l u e}{4}\right) = \textcolor{g r e e n}{- 1} \left(x - \textcolor{b l u e}{0}\right)$

this is the point slope form above, you can simplify to slope intercept form:

$y = - x + 4$