How to find a slope of a line parallel to the graph of each equation #y=-2/3x - 1#?

1 Answer
Mar 30, 2015

The answer is already written! :)

You'll agree that two lines are parallel if the have the same slope. But if you write a line's equation in the form #y=mx+q#, then #m# is exactly the slope of the line. So, in your case, the slope is #-2/3#. So, every other line with slope #-2/3# is parallel to your line.

In other words, you can change the #q# coefficient as you like, obtaining (all) infinite other lines parallel to yours.

This make sense, since changing the #q# coefficient only translates the line upwards or downwards. This is exactly how you obtain parallel lines to a given one: you take it and you shift it a little bit! :)