### All GRE Math Resources

## Example Questions

### Example Question #111 : Coordinate Geometry

What is the y-intercept of the line that goes through the points (–2, 1) and (5, 6)?

**Possible Answers:**

0

The answer cannot be determined from the given information.

67/7

17/7

–2/7

**Correct answer:**

17/7

The slope can be calculated from m = (y_{2 }–_{ }y_{1})/(x_{2 }– x_{1}) = (6 – 1)/(5 + 2). Having calculated the slope, we can now use point-slope form of a line, y – y_{1 }= m(x – x_{1}), and using the second point (5, 6): y – 6 = (5/7)(x – 5). This can be rearranged into slope-intercept form to obtain: y = (5/7)x + (17/7). Because the equation is now in slope intercept form, we know that the y-intercept is 17/7.

### Example Question #111 : Coordinate Geometry

Find the x-intercept of the equation

**Possible Answers:**

–2

10

0

–10

2

**Correct answer:**

10

The answer is 10.

In order to find the x-intercept we simply let all the y's equal 0

### Example Question #111 : Coordinate Geometry

**Quantity A:**

The -intercept of the line

**Quantity B:**

The -intercept of the line

**Possible Answers:**

The relationship cannot be determined from the information given.

Quantity A is greater

Quantity B is greater

The two quantities are equal.

**Correct answer:**

The two quantities are equal.

The key to these quantitative comparison problems is to figure out the worth of both quantities, or figure out whether evaluating the quantities is even possible. In this case, evaluating the quantities is a fairly straightforward case of figuring out the intercepts of two different lines, which is possible. Therefore, you can already discount "the relationship cannot be determined from the information given".

To solve quantity A: is in form, where is the -intercept. Therefore, the -intercept is equal to .

To solve quantity B: , you have to sole for the intercept. The quickest way to figure out the answer is to remember that the axis exists at the line , therefore to find out where the line crosses the axis, you can set and solve for .

-3.5 = .5x - 1.5

Both quantity A and quantity B , therefore the two quantities are equal.

### Example Question #111 : Coordinate Geometry

What is the -intercept of the following equation?

**Possible Answers:**

**Correct answer:**

To find the -intercept, you must plug in for .

This leaves you with

.

Then you must get you by itself so you add to both sides

.

Then divide both sides by to get

.

For the coordinate point, goes first then and the answer is .