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GRE Subject Test: Math : Coordinate Geometry

Study concepts, example questions & explanations for GRE Subject Test: Math

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All GRE Subject Test: Math Resources

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Example Questions

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Example Question #1 : Slope & Intercept

What is the slope () and the y-intercept (b) of the equation

$y = \frac{1}{6}x -\frac{1}{2}$

Possible Answers:

$m=-\frac{1}{6}$ and $b = -\frac{1}{2}$

$m=-\frac{1}{6}$ and $b = \frac{1}{2}$

$m=\frac{1}{6}$ and $b = \frac{1}{2}$

$m=\frac{1}{6}$ and $b = -\frac{1}{2}$

Correct answer:

$m=\frac{1}{6}$ and $b = -\frac{1}{2}$

Explanation:

The formula to find slope and y-intercept is:

y=mx +b

$m=\frac{1}{6}$ and $b =-\frac{1}{2}$

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Example Question #1 : Slope & Intercept

What is the slope (m) and the y-intercept (b) of the equation

y = 3x+2x-1

Possible Answers:

m = 2 and b =2

m = 3 and b = -1

m = 3 and b =-1

m=5 and b =-1

Correct answer:

m=5 and b =-1

Explanation:

The formula to find slope and y-intercept is:

y=mx +b

y = 3x+2x-1

Combine like terms.

y = 5x -1

m=5 and b = -1

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Example Question #31 : Coordinate Geometry

The points given lie on a line. Find the slope.

-2,0,2,4

8, 5, 2, -1

Possible Answers:

$\frac{-3}{2}$

$\frac{3}{2}$

$\frac{2}{3}$

$-\frac{2}{3}$

Correct answer:

$\frac{-3}{2}$

Explanation:

slope = $\frac{rise}{run}$

rise = changes in y

run = changes in x

-2,0,2,4

8, 5, 2, -1

The change in the coordinates is that the numbers are decreasing by 3 or -3.

The change in the coordinates is that the numbers are increasing by 2 or +2;

slope = $\frac{-3}{2}$

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Example Question #1 : Slope & Intercept

The points given lie on a line. Find the slope.

-8,-4,0,4

2, 5, 8, 11

Possible Answers:

$-\frac{3}{4}$

$\frac{3}{4}$

$-\frac{4}{3}$

$\frac{4}{3}$

Correct answer:

$\frac{3}{4}$

Explanation:

slope = $\frac{rise}{run}$

rise = changes in y

run = changes in x

-8,-4,0,4

2, 5, 8, 11

The change in the coordinates is that the numbers are increasing by 3 or +3.

The change in the coordinates is that the numbers are increasing by 4 or +4.

slope = $\frac{3}{4}$

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Example Question #1 : Slope & Intercept

The points given lie on a line. Find the slope.

-6,-4,-2,0

-3, -3, -3, -3

Possible Answers:

m=2

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

Slope is undefined.

m = 0

Correct answer:

m = 0

Explanation:

slope = $\frac{rise}{run}$

rise = changes in y

run = changes in x

-6,-4,-2,0

-3, -3, -3, -3

There is zero change in the coordinates.

The change in the coordinates is that the numbers are increasing by 2 or +2.

slope = $\frac{0}{2}$

m = 0

If the coordinates are the same, then it will be a horizontal line. The slope of a horizontal line is 0.

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Example Question #11 : Slope & Intercept

Find the slope of a line that passes through A (3,-1) and B (6,5).

Possible Answers:

m=-2

$m=\frac{1}{2}$

m=2

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

Correct answer:

m=2

Explanation:

The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$m = \frac{5-(-1)}{6-3}$

$m = \frac{5+1}{6-3}$

$m = \frac{6}{3}$

m=2

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Example Question #51 : Functions And Graphs

Find the slope of a line that passes through the points S(1,2) and T (6,-8) .

Possible Answers:

m=-2

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

$m=\frac{1}{2}$

m=2

Correct answer:

m=-2

Explanation:

The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$m = \frac{-8-2}{6-1}$

$m = \frac{-10}{5}$

m=-2

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Example Question #11 : Slope & Intercept

Find the slope of a line that passes through the points G(-3,-1) and H (-2,-2) .

Possible Answers:

m=0

m=1

m=-1

Slope is undefined.

Correct answer:

m=-1

Explanation:

The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2} -x_{1}}$

$m= \frac{-2-(-1)}{-2- (-3)}$

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

$m=\frac{-1}{1}$

m=1

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Example Question #11 : Slope & Intercept

What is the slope of the line: 3x-6y=-14

Possible Answers:

m=1

$m=\frac {7}{3}$

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

$m=\frac {1}{2}$

Correct answer:

$m=\frac {1}{2}$

Explanation:

Step 1: The current equation is in standard form, where x and y are both on one side of the equal sign..

Step 2: Change the equation to slope-intercept form.. Move the y to the other side

3x=6y-14

Step 3: Move the constant to the other side:

3x+14=6y

Step 4: Divide by the coefficient in front of :

$\frac {3x+14}{6}=\frac {6y}{6}$

Step 5: Split the left side into two fractions and simplify:

$\frac {3x}{6}+\frac {14}{6}=y$

$\rightarrow \frac {1}{2}x+\frac {7}{3}=y$

Step 6. Locate the slope. The slope is the coefficient of the x term.

The slope is $\frac {1}{2}$ , or $m=\frac {1}{2}$

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Example Question #11 : Slope & Intercept

Find the y-intercept of the equation of a line: x+4y=12

Possible Answers:

b=-3

$b=\frac {1}{3}$

b=3

$b=-\frac {1}{3}$

Correct answer:

b=3

Explanation:

Step 1: Subtract from both sides:

$x-x+4y=-x+12 \implies 4y=-x+12$

Step 2: Divide by the coefficient of the y term..In this case, divide by .

$\frac {4y}{y}=\frac {-x+12}{4}$

Simplify and separate fraction on right side:

$y=-\frac{x}{4}+\frac {12}{4}\implies y=-\frac {1}{4}x+3$

Step 3: Locate the y-intercept (also known as b):

If we compare our equation to the general slope-intercept form: y=mx+b , we see that 3=b ..

The value of is .

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GRE Subject Test: Math : Coordinate Geometry

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Slope & Intercept

Example Question #1 : Slope & Intercept

Example Question #31 : Coordinate Geometry

Example Question #1 : Slope & Intercept

Example Question #1 : Slope & Intercept

Example Question #11 : Slope & Intercept

Example Question #51 : Functions And Graphs

Example Question #11 : Slope & Intercept

Example Question #11 : Slope & Intercept

Example Question #11 : Slope & Intercept

All GRE Subject Test: Math Resources

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