GRE Math : Coordinate Geometry

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Example Questions

Example Question #1 : X And Y Intercept

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

Possible Answers:

–2/7

The answer cannot be determined from the given information.

67/7

17/7

Correct answer:

17/7

Explanation:

The slope can be calculated from m = (y₂–y₁)/(x₂– x₁) = (6 – 1)/(5 + 2). Having calculated the slope, we can now use point-slope form of a line, y – y₁= m(x – x₁), 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.

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Example Question #111 : Coordinate Geometry

Find the x-intercept of the equation $x-y=4y+10$

Possible Answers:

–2

–10

Correct answer:

Explanation:

The answer is 10.

$x-y=4y+10$

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

$x-0=4(0)+10$

$x=10$

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Example Question #301 : Geometry

Quantity A:

The -intercept of the line y = 3x - 4

Quantity B:

The -intercept of the line

y - 3.5 = .5(x-3)

Possible Answers:

The relationship cannot be determined from the information given.

The two quantities are equal.

Quantity B is greater

Quantity A is greater

Correct answer:

The two quantities are equal.

Explanation:

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: y = 3x-4 is in y=mx+b form, where is the -intercept. Therefore, the -intercept is equal to .

To solve quantity B: y-3.5 = .5(x-3) , 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 y = 0 , therefore to find out where the line crosses the axis, you can set y=0 and solve for .

-3.5 = .5(x-3) -3.5 = .5x - 1.5

-2 = .5x

-4 = x

Both quantity A and quantity B = -4 , therefore the two quantities are equal.

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Example Question #302 : Geometry

What is the -intercept of the following equation?

y= 17x -13

Possible Answers:

(13,17)

(0,13)

$\left(\frac{13}{17},0\right)$

(13,0)

$\left(0,\frac{13}{17}\right)$

Correct answer:

$\left(\frac{13}{17},0\right)$

Explanation:

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

This leaves you with

0=17x-13 .

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

(13=17x) .

Then divide both sides by to get

$x=\frac{13}{17}$ .

For the coordinate point, goes first then and the answer is $\left(\frac{13}{17},0\right)$ .

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

What is the slope of the line whose equation is $\dpi{100} \small 8x+12y=20$ ?

Possible Answers:

$\dpi{100} \small \frac{3}{2}$

$\dpi{100} \small 2$

$\dpi{100} \small \frac{2}{3}$

$\dpi{100} \small -\frac{2}{3}$

$\dpi{100} \small -\frac{3}{2}$

Correct answer:

$\dpi{100} \small -\frac{2}{3}$

Explanation:

Solve for $\dpi{100} \small y$ so that the equation resembles the $\dpi{100} \small y=mx+b$ form. This equation becomes $\dpi{100} \small -\frac{2}{3}x+\frac{5}{3}$ . In this form, the $\dpi{100} \small m$ is the slope, which is $\dpi{100} \small -\frac{2}{3}$ .

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

Which of the following equations has a -intercept of ?

Possible Answers:

22x-2y=1

2x^2-16y=5

3y=4x^2-16

y=(x-4)^2-3

4x^2=12y+12

Correct answer:

y=(x-4)^2-3

Explanation:

To find the -intercept, you need to find the value of the equation where x=0 . The easiest way to do this is to substitute in for your value of and see where you get for . If you do this for each of your equations proposed as potential answers, you find that y=(x-4)^2-3 is the answer.

Substitute in for :

y=(0-4)^2-3=(-4)^2-3=16-3=13

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

If is a line that has a -intercept of and an -intercept of , which of the following is the equation of a line that is perpendicular to ?

Possible Answers:

$y=\frac{(-3x-24)}{7}$

$y=\frac{(7x+15)}{3}$

$y=\frac{x+7}{3}$

$y=\frac{(3x+11)}{7}$

$y=\frac{(7-7x)}{3}$

Correct answer:

$y=\frac{(7x+15)}{3}$

Explanation:

If has a -intercept of , then it must pass through the point (0,3) .

If its -intercept is , then it must through the point (7,0) .

The slope of this line is $\frac{0-3}{7-0}=-\frac{3}{7}$ .

Therefore, any line perpendicular to this line must have a slope equal to the negative reciprocal, which is $\frac{7}{3}$ . Only $y=\frac{(7x+15)}{3}$ has a slope of $\frac{7}{3}$ .

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GRE Math : Coordinate Geometry

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : X And Y Intercept

Example Question #111 : Coordinate Geometry

Example Question #301 : Geometry

Example Question #302 : Geometry

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

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

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

All GRE Math Resources

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