GMAT Math : Calculating the equation of a parallel line

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Calculating The Equation Of A Parallel Line

What is the equation of the line that is parallel to and goes through point ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slope. Therefore, the slope of the new line is , as the equation of the original line is  ,with slope .

    and      :

Example Question #2 : Calculating The Equation Of A Parallel Line

Find the equation of a line that is parallel to and passes through the point .

 

Possible Answers:

\dpi{100} \small y=2x-7

\dpi{100} \small y=-2x+7

\dpi{100} \small y=2x+7

\dpi{100} \small y< 2x-7None of the answers are correct.

\dpi{100} \small y=-2x-7

Correct answer:

\dpi{100} \small y=2x-7

Explanation:

The parallel line has the equation \dpi{100} \small 4x-2y=5. We can find the slope by putting the equation into slope-intercept form, y = mx + b, where m is the slope and b is the intercept.  \dpi{100} \small 4x-2y=5 becomes \dpi{100} \small y=2x-\frac{5}{2}, so the slope is 2.

We know that our line must have an equation that looks like \dpi{100} \small y=2x+b. Now we need the intercept. We can solve for b by plugging in the point (4, 1).

1 = 2(4) + b

b = –7

Then the line in question is \dpi{100} \small y=2x-7.

Example Question #3 : Calculating The Equation Of A Parallel Line

Given:

Which of the following is the equation of a line parallel to  that has a y-intercept of ?

Possible Answers:

Correct answer:

Explanation:

Parallel lines have the same slope, so our slope will still be 4. The y-intercept is just the "+b" at the end. In f(x) the y-intercept is 13. In this case, we need to have a y-intercept of -13, so our equation just becomes:

Example Question #4 : Calculating The Equation Of A Parallel Line

Find the equation of the line that is parallel to the  and passes through the point .

Possible Answers:

Correct answer:

Explanation:

Two lines are parallel if they have the same slope. The slope of g(x) is 6, so eliminate anything without a slope of 6.

Recall slope intercept form which is .

We know that the line must have an m of 6 and an (x,y) of (8,9). Plug everything in and go from there.

So we get:

Example Question #5 : Calculating The Equation Of A Parallel Line

Given the function , which of the following is the equation of a line parallel to  and has a -intercept of ?

Possible Answers:

Correct answer:

Explanation:

Given a line  defined by the equation  with slope , any line that is parallel to  also has a slope of . Since , the slope  is  and the slope of any line  parallel to  also has a slope of .

Since  also needs to have a -intercept of , then the equation for  must be 

Example Question #6 : Calculating The Equation Of A Parallel Line

Given the function , which of the following is the equation of a line parallel to  and has a -intercept of ?

Possible Answers:

Correct answer:

Explanation:

Given a line  defined by the equation  with slope , any line that is parallel to  also has a slope of . Since , the slope  is  and the slope of any line  parallel to  also has a slope of .

Since  also needs to have a -intercept of , then the equation for  must be 

Example Question #7 : Calculating The Equation Of A Parallel Line

Given the function , which of the following is the equation of a line parallel to  and has a -intercept of ?

Possible Answers:

Correct answer:

Explanation:

Given a line  defined by the equation  with slope , any line that is parallel to  also has a slope of . Since , the slope  is  and the slope of any line  parallel to  also has a slope of .

Since  also needs to have a -intercept of , then the equation for  must be 

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