2.4: Finding the Equation of Parallel Lines
Pablo is researching different types of exercise to see which gives the best calorie burn. He found that an indoor cycling class can burn up to 150 calories every 10 minutes. The elliptical machine burns 270 calories every 30 minutes. Do these two forms of exercise burn the same amount of calories in an hour?
Guidance
When two lines are parallel, they have the same slope and never intersect. So, if a given line has a slope of 2, then any line that is parallel to that line will also have a slope of 2, but it will have a different
Example A
Find the equation of the line that is parallel to
Solution: We know that the slopes will be the same; however we need to find the
The equation of the parallel line is
Example B
Write the equation of the line that passes through (4, 7) and is parallel to
Solution: The line
The same would be true for vertical lines, but all vertical line equations are in the form
Example C
Write the equation of the line that passes through (6, 10) and is parallel to the line that passes through (4, 6) and (3, 4).
Solution: First, we need to find the slope of the line that our line will be parallel to. Use the points (4, 6) and (3, 4) to find the slope.
This is the slope of our given line as well as the parallel line. Use the point (6, 10) to find the
The equation of the line is
Intro Problem Revisit The equation for indoor cycling is
Guided Practice
1. Find the equation of the line that is parallel to
2. Find the equation of the line that is parallel to
3. Find the equation of the line that passes through (5, 2) and is parallel to the line that passes through (6, 1) and (1, 3).
Answers
1. First, we need to change this line from standard form to slopeintercept form.
The equation of the parallel line is
2.
3. First, find the slope between (6, 1) and (1, 3).
This will also be the slope of the parallel line. Use this slope with the given point, (5, 2).
The equation of the parallel line is
Vocabulary
 Parallel
 When two or more lines are in the same plane and never intersect. These lines will always have the same slope.
Practice
Find the equation of the line, given the following information. You may leave your answer in slopeintercept form.
 Passes through (4, 7) and is parallel to
x−y=−5 .  Passes through (6, 2) and is parallel to
y=4 .  Passes through (3, 5) and is parallel to
y=−13x−1 .  Passes through (1, 9) and is parallel to
x=8 .  Passes through the
y− intercept of2x−3y=6 and parallel tox−4y=10 .  Passes through (12, 4) and is parallel to
y=−3x+5 .  Passes through the
x− intercept of2x−3y=6 and parallel tox+4y=−3 .  Passes through (7, 8) and is parallel to
2x+5y=14 .  Passes through (1, 3) and is parallel to the line that passes through (6, 2) and (4, 6).
 Passes through (18, 10) and is parallel to the line that passes through (2, 2) and (8, 1).
 Passes through (4, 1) and is parallel to the line that passes through (15, 7) and (1, 1).
Are the pairs of lines parallel? Briefly explain how you know.

x−2y=4 and−5x+10y=16  \begin{align*}3x + 4y = 8\end{align*} and \begin{align*}6x + 12y = 1\end{align*}
 \begin{align*}5x  5y = 20\end{align*} and \begin{align*}x + y = 7\end{align*}
 \begin{align*}8x  12y = 36\end{align*} and \begin{align*}10x  15y = 15\end{align*}
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Here you'll learn how to find the equation of a line that is parallel to a given line.