# How do you determine the equation of the line that is parallel to 7x + 5y = -3?

Jul 18, 2016

A line parallel to $7 x + 5 y = - 3$ will be of type $7 x + 5 y = k$.

#### Explanation:

Let the equation of line be $a x + b y + c = 0$. Writing this in slope intercept form, we have $b y = - a x - c$ or $y = - \frac{a}{b} x - \frac{c}{b}$ and as such its slope is $- \frac{a}{b}$.

As slopes of two parallel lines are equal, a line parallel to $a x + b y + c = 0$ will also have a slope of $- \frac{a}{b}$ and hence using door intercept form, its equation should be $y = - \frac{a}{b} x + {k}_{1}$ or

$b y = - a x + b {k}_{1}$ or say

$a x + b y - b {k}_{1} = 0$ or

Say $a x + b y + k = 0$.

Hence a line parallel to $a x + b y + c = 0$ will be of type $a x + b y + k = 0$.

Hence a line parallel to $7 x + 5 y = - 3$ will be of type $7 x + 5 y = k$.