# How do you write a linear equation that goes through (1,-6) and is parallel to the line x + 2y = 6?

Mar 5, 2018

$x + 2 y + 11 = 0$

is the required equation of the line.

#### Explanation:

$x + 2 y = 6 \text{ " " } \left(1\right)$

The slope of the line $= - \frac{1}{2}$

The slope of a line parallel to line (1) will be same

$\text{slope} = m = - \frac{1}{2}$

Now, the equation of the line through $\left(1 , - 6\right)$ with a slope $m = - \frac{1}{2}$ by using the point-slope form is

$y - {y}_{1} = m \left(x - {x}_{1}\right)$

$y - \left(- 6\right) = - \frac{1}{2} \left(x - 1\right)$

$y + 6 = - \frac{1}{2} \left(x - 1\right)$

$2 y + 12 = - x + 1$

or

$x + 2 y + 11 = 0$