Question

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

Answer 1

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

Explanation:

Let the equation of line be `ax+by+c=0`. Writing this in slope intercept form, we have `by=-ax-c` or `y=-a/bx-c/b` and as such its slope is `-a/b`.

As slopes of two parallel lines are equal, a line parallel to `ax+by+c=0` will also have a slope of `-a/b` and hence using door intercept form, its equation should be `y=-a/bx+k_1` or

`by=-ax+bk_1` or say

`ax+by-bk_1=0` or

Say `ax+by+k=0`.

Hence a line parallel to `ax+by+c=0` will be of type `ax+by+k=0`.

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