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SAT II Math I : Slope

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #1 : Slope

What is the slope of the line depicted by this equation?

$\small 4x+5y=14$

Possible Answers:

$\small \frac{4}{5}$

$\small -\frac{4}{5}$

$\small \frac{5}{4}$

$\small \frac{14}{5}$

Correct answer:

$\small -\frac{4}{5}$

Explanation:

This equation is written in standard form, that is, $\small Ax+By=C$ where the slope is equal to $\small \frac{-A}{B}$ .

$\small 4x+5y=14$

In this instance $\small A=4$ and $\small B=5$

$m=-\frac{A}{B}=-\frac{4}{5}$

This question can also be solved by converting the slope-intercept form: $\small y=-\frac{4}{5}x+\frac{14}{5}$ .

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Example Question #2 : Slope

Find the slope of the line

4x+3y=-12

Possible Answers:

$\frac{-3}{4}$

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{-4}{3}$

Correct answer:

$\frac{-4}{3}$

Explanation:

To find the slope of any line, we must get the equation into the form

y=mx+b

where m is the slope and b is the y-intercept.

To manipulate our equation into this form, we must solve for y. First, we must move the x term to the right side of our equation by subtracting it from both sides.

(4x+3y)-4x = (-12)-4x

3y = -4x-12

To isolate y, we now must divide each side by 3.

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

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

Now our equation is in the desired form. The coefficient of our x term is our slope, . Therefore

$m = \frac{-4}{3}$

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Example Question #1 : Slope

$\frac{y}{2}=5x-1$

What is the slope of the function above?

Possible Answers:

Correct answer:

Explanation:

First you must get the formula into slope-intercept form which means having by itself,

y=mx+b where is the slope.

You must multiple both sides by to get,

y=10x-2 .

The slope is the value being multiplied by the variable, so our slope is .

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Example Question #4 : Slope

Find the slope of the following equation: 3x+3y =1

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

In order to find the slope, we will need to rearrange the equation so that it is in slope-intercept form y=mx+b .

Subtract on both sides.

3x+3y -3x=1-3x

3y=-3x+1

Divide by three on both sides.

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

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

This equation is now in the form of y=mx+b , where is the slope.

The slope is .

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Example Question #2 : Slope

What is the slope of the following equation? 2y = 3-7x

Possible Answers:

$-\frac{7}{2}$

$\frac{3}{2}$

Correct answer:

$-\frac{7}{2}$

Explanation:

The given equation will need to be rewritten in slope intercept format.

y=mx+b

Divide by two on both sides.

$\frac{2y }{2}=\frac{ 3-7x}{2}$

Rearrange the right side by order of powers.

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

The slope can be seen as $-\frac{7}{2}$

The answer is: $-\frac{7}{2}$

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Example Question #41 : Properties Of Functions And Graphs

What is the slope of the given equation? $y=-\frac{1}{2x}+3$

Possible Answers:

$-\frac{1}{2}$

$\textup{The slope does not exist.}$

Correct answer:

$\textup{The slope does not exist.}$

Explanation:

The slope in a linear equation is defined as y=mx+b .

The x-variable exists in the denominator, which refers to the parent function of:

$y=\frac{1}{x}$

This function is not linear, and will have changing slope along its domain.

The answer is: $\textup{The slope does not exist.}$

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SAT II Math I : Slope

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Slope

Example Question #2 : Slope

Example Question #1 : Slope

Example Question #4 : Slope

Example Question #2 : Slope

Example Question #41 : Properties Of Functions And Graphs

All SAT II Math I Resources

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