Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.5 - More on Slope - Exercise Set - Page 227: 33


The slopes of parallel lines are equal.

Work Step by Step

The slope of a line is the rate of change of its y coordinate with respect to its x coordinate. In other words, it is basically a measure of the steepness of the line. In case of two parallel lines, they have the same steepness. So they must have equal slopes. The slope of parallel line is equal: ${{m}_{1}}={{m}_{2}}$ The converse is also true -- that is, if two lines have the same slope, they must be parallel. Consider the following example: Consider, the equations $y=3x+4\,\,\text{ and }\,\,y=3x-4$ of two non-vertical parallel lines with $y-\text{intercepts}\,\,\,\left( 0,4 \right)\,\text{ and }\,\left( 0,-4 \right)$ respectively. In the above equations $y=3x+4\,\,\text{ and }\,\,y=3x-4$, the slope of the line is the coefficient of x. So, the slope of both lines is $m=3$. From the graph, one can conclude that both lines given by the equations $y=3x+4\,\,\text{ and }\,\,y=3x-4$ are parallel. So they have the same slope, that is $m=3$. Hence, if the lines are parallel, then they have the same slope.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.