How to Find a Parallel Line

By Brenda Sanders; Updated April 24, 2017
Lines with the same slope but different intercepts will be parallel.

To find a parallel line to a given line, you must know how to write an equation of a line. You must also know how to put the equation of a line in slope-intercept form. Additionally, you must know how to identify the slope and the Y-intercept in the equation of a line. It is important to remember that parallel lines have equal slopes. Learn how to be able to find a parallel line.

Look at the equation of the line. Let’s say “3x + y = 8” is the equation of the given line. Put the equation of the given line in slope-intercept form: y = mx + b. Using “3x + y = 8” as the equation of the given line, put the equation in slope-intercept form by solving for "y" (subtracting -3x from both sides). You will get “y = -3x + 8.”

Identify the slope. The slope is the "m" in “y = mx + b.” Therefore, the slope in “y = -3x + 8 (slope-intercept form of the given line),” is -3. Identify the y-intercept. The y-intercept is the b in “y = mx + b.” Therefore, the y-intercept in “y = -3x + 8 (slope-intercept form of the given line),” is 8.

Change the y-intercept to any constant number. This will yield a parallel line since you will not change the slope or anything else in the equation. The slopes of parallel lines are equal. Using the given equation of a line “y = -3x + 8 (slope-intercept form),” change the y-intercept of 8 to a 9. You will get “y = -3x + 9 (slope-intercept form).” The parallel line is "y = -3x + 9 (slope-intercept form).” This means that “y = -3x + 9 (slope-intercept form)" is parallel to “y = -3x + 8 (slope-intercept form).”

About the Author

Brenda Sanders is an educator who has taught in many capacities for over 15 years. She recently completed her doctorate in education from George Fox University. Brenda received her MAT from Pacific University and a Bachelor of Arts degree in journalism from California State University, Long Beach. She has also worked as a proofreader, editor and writer.