# How do you draw the line that is parallel to y=-1/2x+5 and passes through the point (2, -3)?

Mar 26, 2018

The equation of the line parallel to $y = - \frac{1}{2} x + 5$ that passes through the point $\left(2 , - 3\right)$ is $y = - \frac{1}{2} x - 2$.

#### Explanation:

The slope of the line parallel to another line is the same as that of the other line. Therefore, the slope of the line parallel to $y = - \frac{1}{2} x + 5$ is $- \frac{1}{2}$ because the slope of that line is $- \frac{1}{2}$.

Using point-slope form, $y - {y}_{1} = m \left(x - {x}_{1}\right)$ where $y - 1$ and ${x}_{1}$ are points from a given coordinate pair $\left(x , y\right)$ that lies on the line, and $m$ is the slope.

Plugging in $- \frac{1}{2}$ for $m$, $2$ for ${x}_{1}$, and $- 3$ for ${y}_{1}$:
$y - \left(- 3\right) = - \frac{1}{2} \left(x - 2\right)$
$y + 3 = - \frac{1}{2} x + 1$
$y = - \frac{1}{2} x - 2$