Slope & Intercept - GRE Quantitative Reasoning

Card 0 of 68

Question

What is the slope and y-intercept of this line: ?

Answer

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

$\rightarrow 3x=12+4y$

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

$\rightarrow 3x-12=4y$

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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Question

Find the slope of a line that passes through and

Answer

The formula for slope is:

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

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

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

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

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Question

Find the slope of a line that passes through the points and .

Answer

The formula for slope is:

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

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

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

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Question

Find the slope of a line that passes through points and .

Answer

The formula for slope is:

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

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

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

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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Question

Find the slope of a line that passes through points and

Answer

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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Question

Find the slope of a line that passes through the points and .

Answer

The formula for slope is:

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

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

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

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

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Question

Find the slope of a line that passes through points and

Answer

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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Question

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

Answer

Subtract from both sides of the equation.

Write equation in the form of .

( represents the y-intercept)

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Question

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

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

Answer

The formula to find slope and y-intercept is:

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

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Question

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

Answer

The formula to find slope and y-intercept is:

Combine like terms.

and

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Question

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

Answer

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

rise = changes in y

run = changes in x

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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Question

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

Answer

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

rise = changes in y

run = changes in x

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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Question

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

Answer

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

rise = changes in y

run = changes in x

There is zero change in the coordinates.

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

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

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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Question

What is the slope of the line:

Answer

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

Step 3: Move the constant to the other side:

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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Question

Find the y-intercept of the equation of a line:

Answer

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: , we see that ..

The value of is .

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Question

What is the slope of the line: $2x-4y-8=0$

Answer

Step 1: Move the $4y$ to the other side...

$2x-8=4y$

Step 2: Divide by $4$ on both sides...

$\frac {2x-8}{4}=y-> \frac {2x}{4}-\frac {8}{4}=y->\frac {x}{2}-2=y$

The slope is $\frac {1}{2}$ .

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Question

What is the y-intercept of the equation ?

Answer

Step 1: Recall what the basic equation is for a line in slope-intercept form..

m=slope, b=y-intercept...

Step 2: Find m and b in the equation given...

m=, b=..

b=y-intercept=

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Question

What is the slope and y-intercept of this line: ?

Answer

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

$\rightarrow 3x=12+4y$

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

$\rightarrow 3x-12=4y$

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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Question

Find the slope of a line that passes through and

Answer

The formula for slope is:

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

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

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

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

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Question

Find the slope of a line that passes through the points and .

Answer

The formula for slope is:

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

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

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

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