# How do you write the equation of the line passing through ( 3, - 2) and parallel to : x + 7y - 5 = 0?

Apr 12, 2018

$7 y + x + 11 = 0$

#### Explanation:

We first find the slope of the original line, then use our slope and point to find our equation.

Slope-intercept form is a way of writing your linear equation. It is of the form $y = m x + b$, where $m$ is the slope and $b$ is the initial value.

If two lines are parallel, then they have the same slope. Our given equation is $x + 7 y - 5 = 0$, which can be written in slope-intercept form as $y = - \frac{1}{7} x + \frac{5}{7}$. The slope of both lines, then, is $- \frac{1}{7}$.

Now we use slope-intercept form again to find our new equation given our point $\left(3 , - 2\right)$ and our slope $m = - \frac{1}{7}$. We plug in and solve for $b$,

$y = m x + b$
$y = - \frac{1}{7} x + b$
$- 2 = - \frac{1}{7} \left(3\right) + b$
$- 2 + \frac{3}{7} = b$
$b = - \frac{11}{7}$

Thus, our desired equation is $y = - \frac{1}{7} x - \frac{11}{7}$. Our original equation was in standard form, so we should put our answer in standard form.

$y = - \frac{1}{7} x - \frac{11}{7}$
$7 y = - x - 11$
$7 y + x + 11 = 0$

Our final answer is $7 y + x + 11 = 0$.