# How do you write an equation in point slope and slope intercept form parallel to y=1/2x-1 point: (0,-4)?

Oct 11, 2016

$y + 4 = \frac{1}{2} \left(x - 0\right)$

#### Explanation:

Point slope form is $y - \textcolor{b l u e}{{y}_{1}} = \textcolor{m a \ge n t a}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$
where $\textcolor{m a \ge n t a}{m} =$ slope and $\left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ is a point.

Parallel lines have the same slope. The equation
$y = \textcolor{m a \ge n t a}{\frac{1}{2}} x - 1$ is in the form $y = \textcolor{m a \ge n t a}{m} x + b$ where $\textcolor{m a \ge n t a}{m} =$slope.

The slope in this example is $\textcolor{m a \ge n t a}{\frac{1}{2}}$, and the parallel slope is also $\textcolor{m a \ge n t a}{\frac{1}{2}}$.

The point $\left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$ is $\left(\textcolor{red}{0} , \textcolor{b l u e}{- 4}\right)$.

So the equation in point slope form is

$y - \textcolor{b l u e}{- 4} = \textcolor{m a \ge n t a}{\frac{1}{2}} \left(x - \textcolor{red}{0}\right)$

$y + 4 = \frac{1}{2} \left(x - 0\right)$