### All GMAT Math Resources

## Example Questions

### Example Question #1 : Calculating X Or Y Intercept

What is the -intercept of the line ?

**Possible Answers:**

**Correct answer:**

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:**

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:**

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:**

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 :

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:**

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:**

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:**

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 #8 : Calculating X Or Y Intercept

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

**Possible Answers:**

The graph has no -intercept.

**Correct answer:**

Substitute 0 for :

The -intercept is

### Example Question #9 : Calculating X Or Y Intercept

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

**Possible Answers:**

**Correct answer:**

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 #10 : 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.

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.