All GRE Math Resources
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)?
–2/7
67/7
The answer cannot be determined from the given information.
17/7
0
17/7
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.
Example Question #111 : Coordinate Geometry
Find the x-intercept of the equation
0
2
–2
10
–10
10
The answer is 10.
In order to find the x-intercept we simply let all the y's equal 0
Example Question #1 : X And Y Intercept
Quantity A:
The -intercept of the line
Quantity B:
The -intercept of the line
Quantity A is greater
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater
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 #1 : X And Y Intercept
What is the -intercept of the following equation?
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
.
Example Question #2 : X And Y Intercept
What is the slope of the line whose equation is ?
Solve for so that the equation resembles the
form. This equation becomes
. In this form, the
is the slope, which is
.
Example Question #1 : How To Find The Equation Of A Curve
Which of the following equations has a -intercept of
?
To find the -intercept, you need to find the value of the equation where
. 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
is the answer.
Substitute in for
:
Example Question #1 : 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
?
If has a
-intercept of
, then it must pass through the point
.
If its -intercept is
, then it must through the point
.
The slope of this line is .
Therefore, any line perpendicular to this line must have a slope equal to the negative reciprocal, which is . Only
has a slope of
.
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