Question

How do you find the slope parallel to `3y=-2x+5`?

Answer 1

Finding the slope parallel to this line means finding the slope of this line, since parallel lines are defined as lines with the same slope!

In this case the slope is `m=-2/3`.

Explanation:

First rearrange the equation of the line into slope-intercept form, `y=mx+c`. Then `m` is the slope and `c` is the y-intercept.

In this case this basically just requires dividing both sides by 3:

`y=-2/3x+5/3`

The slope, `m`, is simply `-2/3`.

(note that I have solved this question in 2-dimensional space. In 3D (or higher) it gets a little more complex but the principles are the same)