High School Math : How to find the equation of a parallel line

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Find The Equation Of A Parallel Line

What line is parallel to through the point ?

Possible Answers:

Correct answer:

Explanation:

The given line can be rewritten as , which has slope .

If the new line is parallel to the old line, it must have the same slope.  So we use the point-slope form of an equation to calculate the new intercept.

becomes where .

So the equation of the parallel line is .

Example Question #2 : How To Find The Equation Of A Parallel Line

Find the equation of a line parallel to

Possible Answers:

Correct answer:

Explanation:

Since parallel lines share the same slope, the only answer that works is 

Example Question #3 : How To Find The Equation Of A Parallel Line

Given the equation  and the point , find a line through the point that is parallel to the given line. 

Possible Answers:

Correct answer:

Explanation:

In order for two lines to be parallel, they must have the same slope. The slope of the given line is , so we know that the line going through the given point also has to have a slope of . Using the point-slope formula,

,

where  represents the slope and  and  represent the given points, plug in the points given and simplify into standard form:

Example Question #4 : How To Find The Equation Of A Parallel Line

What line is parallel to through ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slopes.  The slope for the given equation is .  We can use the slope and the new point in the slope intercept equation to solve for the intercept:

 

 

Therefore the new equation becomes:

Example Question #5 : How To Find The Equation Of A Parallel Line

What line is parallel to through ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slope.  The slope of the given line is .

Find the line with slope through the point  by plugging this informatuon into the slope intercept equation, :

, which gives .

Solve for by subtracting from both sides to get .

Then the parallel line equation becomes , and converting to standard form gives .

Example Question #6 : How To Find The Equation Of A Parallel Line

Find the equation of a line parallel to the line that goes through points  and .

Possible Answers:

Correct answer:

Explanation:

Parallel lines share the same slope. Because the slope of the original line is , the correct answer must have that slope, so the correct answer is

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