# What is the equation in point-slope form of the line passing through (0, 2) and (1, 5)?

May 10, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line. 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:

$m = \frac{\textcolor{red}{5} - \textcolor{b l u e}{2}}{\textcolor{red}{1} - \textcolor{b l u e}{0}} = \frac{3}{1} = 3$

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 $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

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

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{3} \left(x - \textcolor{red}{0}\right)$

Or

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{3} x$

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

$\left(y - \textcolor{red}{5}\right) = \textcolor{b l u e}{3} \left(x - \textcolor{red}{1}\right)$