GRE Math : Geometry

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Example Questions

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

What is the slope of a line passing through the point (12,-4) , if it is defined by:

y=mx+7 ?

Possible Answers:

$\frac{12}{7}$

$\frac{-7}{12}$

$\frac{-11}{12}$

$\frac{-1}{7}$

$\frac{11}{12}$

Correct answer:

$\frac{-11}{12}$

Explanation:

Since the equation is defined as it is, you know the y-intercept is . This is the point (0,7) . To find the slope of the line, you merely need to use the two points that you have and find the equation:

$\frac{rise}{run}=\frac{-4-7}{12-0}=\frac{-11}{12}$

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Example Question #3 : How To Find The Slope Of A Line

Line1

Which of the following could be an equation for the red line pictured above?

Possible Answers:

y=4x+3

y=-4x-2

y=15x+12

y=-3x+3

y=5x-4

Correct answer:

y=-3x+3

Explanation:

There are two key facts to register about this drawing. First, the line clearly has a negative slope, given that it runs "downhill" when you look at it from left to right. Secondly, it has a positive y-intercept. Therefore, you know that the coefficient for the term must be negative, and the numerical coefficient for the y-intercept must be positive. This only occurs in the equation y=-3x+3 . Therefore, this is the only viable option.

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Example Question #2 : How To Find The Slope Of A Line

What is the slope of a line defined by the equation:

14x-3y+3=10x+4y-10

Possible Answers:

$\frac{7}{10}$

$-\frac{4}{7}$

$\frac{5}{6}$

$\frac{4}{7}$

$-\frac{10}{7}$

Correct answer:

$\frac{4}{7}$

Explanation:

A question like this is actually rather easy. All you need to do is rewrite the equation in slope intercept form, that is:

y=mx+b

Therefore, begin to simplify:

14x-3y+3=10x+4y-10

Becomes...

-3y-4y=10x-14x-10-3

Then...

-7y=-4x-13

Finally, divide both sides by :

$y=\frac{4x}{7}+\frac{13}{7}$

The coefficient for the term is your slope: $\frac{4}{7}$

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Example Question #3 : How To Find The Slope Of A Line

What is the slope of line 3 = 8y - 4x?

Possible Answers:

0.5

-0.5

-2

Correct answer:

0.5

Explanation:

Solve equation for y. y=mx+b, where m is the slope

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Example Question #31 : Lines

Find the slope of the line 6X – 2Y = 14

Possible Answers:

-3

-6

Correct answer:

Explanation:

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

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Example Question #4 : How To Find The Slope Of A Line

If 2x – 4y = 10, what is the slope of the line?

Possible Answers:

–2

0.5

–5/2

–0.5

Correct answer:

0.5

Explanation:

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

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Example Question #21 : Other Lines

What is the slope of the line with equation 4x – 16y = 24?

Possible Answers:

–1/4

1/2

1/8

1/4

–1/8

Correct answer:

1/4

Explanation:

The equation of a line is:

y = mx + b, where m is the slope

4x – 16y = 24

–16y = –4x + 24

y = (–4x)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

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Example Question #3 : Other Lines

What is the slope of a line which passes through coordinates $\dpi{100} \small (3,7)$ and $\dpi{100} \small (4,12)$ ?

Possible Answers:

$\dpi{100} \small 3$

$\dpi{100} \small \frac{1}{5}$

$\dpi{100} \small 2$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small 5$

Correct answer:

$\dpi{100} \small 5$

Explanation:

Slope is found by dividing the difference in the $\dpi{100} \small y$ -coordinates by the difference in the $\dpi{100} \small x$ -coordinates.

$\dpi{100} \small \frac{(12-7)}{(4-3)}=\frac{5}{1}=5$

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Example Question #41 : Coordinate Geometry

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

Possible Answers:

$16$

$6$

$-16$

$\frac{8}{3}$

$\frac{7}{6}$

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 #222 : Geometry

What is the slope of the given linear equation?

2x + 4y = -7

Possible Answers:

-2

1/2

-1/2

-7/2

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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GRE Math : Geometry

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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

Example Question #3 : How To Find The Slope Of A Line

Example Question #2 : How To Find The Slope Of A Line

Example Question #3 : How To Find The Slope Of A Line

Example Question #31 : Lines

Example Question #4 : How To Find The Slope Of A Line

Example Question #21 : Other Lines

Example Question #3 : Other Lines

Example Question #41 : Coordinate Geometry

Example Question #222 : Geometry

All GRE Math Resources

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