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GRE Subject Test: Math : Slope & Intercept

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

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Example Questions

Example Question #1 : Slope & Intercept

What is the slope and y-intercept of this line: 3x-4y=12 ?

Possible Answers:

$Slope=\frac {3}{4},y-intercept=3$

$Slope=\frac {4}{3},y-intercept=3$

$Slope=\frac {-3}{4},y-intercept=3$

$Slope=\frac {3}{4},y-intercept=2$

Correct answer:

$Slope=\frac {3}{4},y-intercept=3$

Explanation:

Step 1: Move the y-term to the other side. We will add 4y.

3x-4y+(4y)=12+(4y)
$\rightarrow 3x=12+4y$

Step 2: Move the constant to the other side. We will subtract 12.

3x+(-12)=12+(-12)+4y
$\rightarrow 3x-12=4y$

Step 3: Divide by the coefficient in front of the y term. In this question, we divide all terms by 4.

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

$\rightarrow y=\frac {3}{4}x-3$

Step 4: Identify the slope and the y-intercept. The slope is the number that is in front of the x term, and the y-intercept is the number that comes after the x-term.

In this question, the slope is $\frac {3}{4}$ and the y-intercept is .

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Example Question #1 : Slope & Intercept

Find the slope of a line that passes through points Y(-5,-1) and Z(3,-1) .

Possible Answers:

m = 8

m=0

Slope is undefined.

m=-8

Correct answer:

m=0

Explanation:

The formula for slope is:

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

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

$m=\frac{0}{8}$

m=0

When the y coordinates are the same, as in this case both were -1, this would form a horizontal line. The slope of a horizontal line is zero.

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Example Question #1 : Slope & Intercept

Find the slope of a line that passes through points X(4,2) and Y (4,1).

Possible Answers:

Slope is undefined.

m=0

m=-3

m=3

Correct answer:

Slope is undefined.

Explanation:

The formula for slope is:

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

$m = \frac{-1-2}{4-4}$

$m= \frac{-3}{0}$

Slope is undefined.

If the x coordinates are the same, as in this problem both x coordinates are 4, then this will be a vertical line. The slope of a vertical line is undefined.

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Example Question #2 : Slope & Intercept

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

Possible Answers:

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

m=0

Slope is undefined.

$m=\frac{5}{2}$

Correct answer:

$m=\frac{5}{2}$

Explanation:

The formula for slope is:

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

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

$m = \frac{5}{2}$

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Example Question #45 : Functions And Graphs

What is the slope and y-intercept of the following equation?

x+y =4

Possible Answers:

m=-4 and b = -1

m = -1 and b = 4

m=1 and b =1

m= 4 and b = -1

Correct answer:

m = -1 and b = 4

Explanation:

x + y = 4

Subtract from both sides of the equation.

y = 4-x

Write equation in the form of y=mx +b .

y = -1x +4

m= -1

b = 4 ( represents the y-intercept)

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Example Question #2 : 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 #47 : Functions And Graphs

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

y = 3x+2x-1

Possible Answers:

m = 3 and b =-1

m=5 and b =-1

m = 2 and b =2

m = 3 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 #48 : Functions And Graphs

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 #49 : Functions And Graphs

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

-8,-4,0,4

2, 5, 8, 11

Possible Answers:

$\frac{3}{4}$

$\frac{4}{3}$

$-\frac{3}{4}$

$-\frac{4}{3}$

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 #9 : Slope & Intercept

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

-6,-4,-2,0

-3, -3, -3, -3

Possible Answers:

Slope is undefined.

m = 0

m=2

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

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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GRE Subject Test: Math : Slope & Intercept

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 #1 : Slope & Intercept

Example Question #2 : Slope & Intercept

Example Question #45 : Functions And Graphs

Example Question #2 : Slope & Intercept

Example Question #47 : Functions And Graphs

Example Question #48 : Functions And Graphs

Example Question #49 : Functions And Graphs

Example Question #9 : Slope & Intercept

All GRE Subject Test: Math Resources

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