# How do you write the equation in point slope form given (-3,4) and (4,-3)?

Aug 3, 2017

See a solution process below:

#### Explanation:

FIrst, we need to determine the slope. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{4}}{\textcolor{red}{4} - \textcolor{b l u e}{- 3}} = \frac{\textcolor{red}{- 3} - \textcolor{b l u e}{4}}{\textcolor{red}{4} + \textcolor{b l u e}{3}} = - \frac{7}{7} = - 1$

We can now use the point-slope formula to write the equation for the line. The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\left(\textcolor{red}{{x}_{1} , {y}_{1}}\right)$ is a point the line passes through.

Substituting the slope we calculated and the values from the first point in the problem gives:

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{- 3}\right)$

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{- 1} \left(x + \textcolor{red}{3}\right)$

Or

$\left(y - \textcolor{red}{4}\right) = \textcolor{b l u e}{-} \left(x + \textcolor{red}{3}\right)$

We can also substitute the slope we calculated and the values from the second point in the problem giving:

$\left(y - \textcolor{red}{- 3}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{4}\right)$

$\left(y + \textcolor{red}{3}\right) = \textcolor{b l u e}{- 1} \left(x - \textcolor{red}{4}\right)$

Or

$\left(y + \textcolor{red}{3}\right) = \textcolor{b l u e}{-} \left(x - \textcolor{red}{4}\right)$