GMAT Math : Calculating x or y intercept

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #1 : Calculating X Or Y Intercept

What is the -intercept of the line  ?

Possible Answers:

Correct answer:

Explanation:

To solve for the x-intercept, substitute 0 for  and solve for 

The -intercept is .

Example Question #2 : Calculating X Or Y Intercept

What is the -intercept of the line  ?

Possible Answers:

Correct answer:

Explanation:

Substitute 0 for  and solve for :

The -intercept is 

Example Question #3 : Calculating X Or Y Intercept

What is the -intercept of a line that includes points  and  ?

Possible Answers:

Correct answer:

Explanation:

The slope of the line is 

Use the point slope form to find the equation of the line.

Now substitute  and solve for .

The -intercept is 

Example Question #4 : Calculating X Or Y Intercept

Give the area of the region on the coordinate plane bounded by the -axis, the -axis, and the graph of the equation  .

Possible Answers:

Correct answer:

Explanation:

This can best be solved using a diagram and noting the intercepts of the line of the equation , which are calculated by substituting 0 for  and  separately and solving for the other variable.

-intercept:

-intercept:

Now, we can make and examine the diagram below - the red line is the graph of the equation :

Triangle_2

The pink triangle is the one whose area we want; it is a right triangle whose legs, which can serve as base and height, are of length . We can compute its area:

Example Question #5 : Calculating X Or Y Intercept

What is the -intercept of

Possible Answers:

Correct answer:

Explanation:

To solve for the -intercept, you have to set  to zero and solve for :

Example Question #6 : Calculating X Or Y Intercept

What is -intercept for

Possible Answers:

Correct answer:

Explanation:

To solve for the -intercept, you have to set  to zero and solve for :

Example Question #7 : Calculating X Or Y Intercept

A line with slope  includes point . What is the -intercept of this line in terms of ?

Possible Answers:

Correct answer:

Explanation:

For some real number , the -intercept of the line will be some point . We can set up the slope equation and solve for  as follows:

Example Question #6 : Calculating X Or Y Intercept

Give the -intercept(s) of the graph of the equation

Possible Answers:

The graph has no -intercept.

Correct answer:

Explanation:

Substitute 0 for :

The -intercept is 

Example Question #7 : Calculating X Or Y Intercept

Give the -intercept(s) of the graph of the equation

Possible Answers:

Correct answer:

Explanation:

Set 

Using the -method, we look to split the middle term of the quadratic expression into two terms. We are looking for two integers whose sum is  and whose product is ; these numbers are .

Set each linear binomial to 0 and solve:

or 

There are two -intercepts - 

Example Question #8 : Calculating X Or Y Intercept

A line includes  and . Give its -intercept.

Possible Answers:

The line has no -intercept.

Correct answer:

The line has no -intercept.

Explanation:

The two points have the same  coordinate, which is 5; the line is therefore vertical. This makes the line parallel to the -axis, meaning that it does not intersect it. Therefore, the line has no -intercept.

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