GRE Math : Coordinate Geometry

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Example Question #116 : Coordinate Geometry

What is the slope of the line represented by the equation $6y-16x=7$ ?

Possible Answers:

$\frac{8}{3}$

$16$

$-16$

$6$

$\frac{7}{6}$

Correct answer:

$\frac{8}{3}$

Explanation:

To rearrange the equation into a $y=mx+b$ format, you want to isolate the $y$ so that it is the sole variable, without a coefficient, on one side of the equation.

First, add $11x$ to both sides to get $6y=7+16x$ .

Then, divide both sides by 6 to get $y=\frac{7+16x}{6}$ .

If you divide each part of the numerator by 6, you get $y=\frac{7}{6}+\frac{16x}{6}$ . This is in a $y=b+mx$ form, and the $m$ is equal to $\frac{16}{6}$ , which is reduced down to $\frac{8}{3}$ for the correct answer.

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Example Question #117 : Coordinate Geometry

What is the slope of the given linear equation?

2x + 4y = -7

Possible Answers:

1/2

-2

-7/2

-1/2

Correct answer:

-1/2

Explanation:

We can convert the given equation into slope-intercept form, y=mx+b, where m is the slope. We get y = (-1/2)x + (-7/2)

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Example Question #91 : Algebra

What is the slope of the line:

$\frac{14}{3}x=\frac{1}{6}y-7$

Possible Answers:

$\frac{1}{28}$

$-\frac{1}{28}$

Correct answer:

Explanation:

First put the question in slope intercept form (y = mx + b):

–(1/6)y = –(14/3)x – 7 =>

y = 6(14/3)x – 7

y = 28x – 7.

The slope is 28.

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Example Question #119 : Coordinate Geometry

What is the slope of a line that passes though the coordinates $(5,2)$ and $(3,1)$ ?

Possible Answers:

$-\frac{1}{2}$

$-\frac{2}{3}$

$\frac{2}{3}$

$4$

$\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

$m=\frac{y_2-y_1}{x_2-x_1}$

Use the give points in this formula to calculate the slope.

$m=\frac{1-2}{3-5}=\frac{-1}{-2}=\frac{1}{2}$

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Example Question #1 : How To Find The Slope Of A Line

What is the slope of a line running through points (7,3) and (8,-4) ?

Possible Answers:

$\frac{7}{3}$

$-\frac{1}{7}$

Correct answer:

Explanation:

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

$m=\frac{y_2-y_1}{x_2-x_1}$

Use the give points in this formula to calculate the slope.

$m=\frac{3-(-4)}{7-8}=\frac{7}{-1}=-7$

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Example Question #231 : Geometry

Find the point where the line y = .25(x – 20) + 12 crosses the x-axis.

Possible Answers:

(0,–28)

(12,0)

(–28,0)

(–7,0)

(0,0)

Correct answer:

(–28,0)

Explanation:

When the line crosses the x-axis, the y-coordinate is 0. Substitute 0 into the equation for y and solve for x.

.25(x – 20) + 12 = 0

.25x – 5 = –12

.25x = –7

x = –28

The answer is the point (–28,0).

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Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

On a coordinate plane, two lines are represented by the equations y=x+3 and y=2x+5 . These two lines intersect at point . What are the coordinates of point ?

Possible Answers:

(2,-1)

(-1,2)

(1,-2)

(-2,-1)

(-2,1)

Correct answer:

(-2,1)

Explanation:

You can solve for the within these two equations by eliminating the . By doing this, you get x+3=2x+5 .

Solve for to get and plug back into either equation to get the value of as 1.

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Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

If the two lines represented by y=x+4 and y=3x-8 intersect at point , what are the coordinates of point ?

Possible Answers:

(6,10)

(2,4)

(4,8)

(6,8)

(2,6)

Correct answer:

(6,10)

Explanation:

Solve for by setting the two equations equal to one another:

x+4=3x-8

x=6

Plugging back into either equation gives y=10 .

These are the coordinates for the intersection of the two lines.

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Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Determine the greater quantity:

BD+AC-BC

Possible Answers:

The relationship cannot be determined.

The quantities are equal.

BD+AC-BC

Correct answer:

The quantities are equal.

Explanation:

$\dpi{100} \small BD+AC$ is the length of the line, except that $\dpi{100} \small BC$ is double counted. By subtracting $\dpi{100} \small BC$ , we get the length of the line, or $\dpi{100} \small AD$ .

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Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Which of the following set of points is on the line formed by the equation 3x-6y=12 ?

Possible Answers:

(6,0)

(-1,3)

(-4,-2)

(4,0)

(-2,-4)

Correct answer:

(4,0)

Explanation:

The easy way to solve this question is to take each set of points and put it into the equation. When we do this, we find the only time the equation balances is when we use the points (4,0) .

3x-6y=12

3(4)-6(0)=12

12-0=12

12=12

For practice, try graphing the line to see which of the points fall on it.

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GRE Math : Coordinate Geometry

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #116 : Coordinate Geometry

Example Question #117 : Coordinate Geometry

Example Question #91 : Algebra

Example Question #119 : Coordinate Geometry

Example Question #1 : How To Find The Slope Of A Line

Example Question #231 : Geometry

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

All GRE Math Resources

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