Suppose a coordinate plane were transposed over the map of a city, and Main Street had the equation
Guidance
In a previous Concept, you learned how to identify parallel lines.
Parallel lines have the same slope.
Each of the graphs below have the same slope, which is 2. According to the definition, all these lines are parallel.
Example A
Are
Solution: The slope of the first line is
Find the slope of the second equation:
These two lines have the same slope so they are parallel.
Writing Equations of Parallel Lines
Sometimes, you will asked to write the equation of a line parallel to a given line that goes through a given point. In the following example, you will see how to do this.
Example B
Find the equation parallel to the line
Solution:
Parallel lines have the same slope, so the slope will be 6. You have a point and the slope, so you can use pointslope form.
You could rewrite it in slopeintercept form:
Example C
Find the equation of the line parallel to the line
Solution:
First, we notice that this equation is in pointslope form, so let's use pointslope form to write this equation.
Guided Practice
Find the equation of the line parallel to the line
Solution:
Since this is in standard form, we must first find the slope. For
Now that we have the slope, we can plug it in:
Practice
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK12 Basic Algebra: Equations of Parallel and Perpendicular Lines (9:13)
 Define parallel lines.
Determine the slope of a line parallel to each line given.

y=−5x+7 
2x+8y=9 
x=8 
y=−4.75 
y−2=15(x+3)
For the following equations, find the line parallel to it through the given point.

y=−35x+2;(0,−2) 
5x−2y=7;(2,−10) 
x=y;(2,3) 
x=−5;(−2,−3)
Mixed Review
 Graph the equation
2x−y=10 .  On a model boat, the stack is 8 inches high. The actual stack is 6 feet tall. How tall is the mast on the model if the actual mast is 40 feet tall?
 The amount of money charged for a classified advertisement is directly proportional to the length of the advertisement. If a 50word advertisement costs $11.50, what is the cost of a 70word advertisement?
 Simplify
112−−−√ .  Simplify
122−72−−−−−−−√ .  Is
3√−2√ rational, irrational, or neither? Explain your answer.  Solve for
s: 15s=6(s+32) .