# How do you write an equation of a line with point (4,2), slope 1/2?

Jan 17, 2017

See the entire process for writing the equation below:

#### Explanation:

We can use the point-slope formula to write an equation for this 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 $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the values from the problem gives:

$\left(y - \textcolor{red}{2}\right) = \textcolor{b l u e}{\frac{1}{2}} \left(x - \textcolor{red}{4}\right)$

We can solve this for the more familiar slope-intercept form by solving for $y$:

$y - \textcolor{red}{2} = \left(\textcolor{b l u e}{\frac{1}{2}} \times x\right) - \left(\textcolor{b l u e}{\frac{1}{2}} \times \textcolor{red}{4}\right)$

$y - \textcolor{red}{2} = \frac{1}{2} x - 2$

$y - \textcolor{red}{2} + 2 = \frac{1}{2} x - 2 + 2$

$y - 0 = \frac{1}{2} x - 0$

$y = \frac{1}{2} x$