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Algebra 1 : How to find inverse variation

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #935 : Functions And Lines

Find the inverse: y=4x-6

Possible Answers:

y=-4x+6

y=-4x-6

$y= -\frac{1}{4}x + \frac{3}{2}$

$y= \frac{1}{4}x + \frac{3}{2}$

$y= \frac{1}{4}x- \frac{3}{2}$

Correct answer:

$y= \frac{1}{4}x + \frac{3}{2}$

Explanation:

To find the inverse, first interchange the x and y variables in the equation.

x=4y-6

Solve for y. Add 6 on both sides.

x+6=4y-6+6

Simplify.

x+6=4y

Divide by four on both sides.

$\frac{x+6}{4}=\frac{4y}{4}$

Simplify both sides.

$y=\frac{x+6}{4} = \frac{1}{4}x + \frac{6}{4}= \frac{1}{4}x + \frac{3}{2}$

The inverse is: $y= \frac{1}{4}x + \frac{3}{2}$

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Example Question #4221 : Algebra 1

Find the inverse of: y=2(x+3)

Possible Answers:

y=-2x-3

$y=\frac{1}{2}x -3$

y=-2x+3

$y=-\frac{1}{2}x -3$

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

Correct answer:

$y=\frac{1}{2}x -3$

Explanation:

Interchange the x and y variables.

x=2(y+3)

Solve for y. First distribute the two inside the parentheses.

x=2y+6

Subtract six from both sides.

x-6=2y+6-6

Simplify.

x-6=2y

Divide by two on both sides.

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

Simplify and reduce.

The answer is: $y=\frac{1}{2}x -3$

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Example Question #171 : Algebraic Functions

Find the inverse of: y=10x-1

Possible Answers:

$y=\frac{1}{10}x +1$

$y=\frac{1}{10}x -1$

$y=-\frac{1}{10}x + \frac{1}{10}$

$y=-\frac{1}{10}x -\frac{1}{10}$

$y=\frac{1}{10}x + \frac{1}{10}$

Correct answer:

$y=\frac{1}{10}x + \frac{1}{10}$

Explanation:

Interchange the x and y variables.

x=10y-1

Solve for y.

Add one on both sides.

x+1=10y-1+1

Simplify both sides.

x+1=10y

Divide by ten on both sides.

$\frac{x+1}{10}=\frac{10y}{10}$

Simplify both sides.

The answer is: $y=\frac{1}{10}x + \frac{1}{10}$

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Example Question #932 : Functions And Lines

Find the inverse of: y=-9x-14

Possible Answers:

$y=- \frac{1}{9}x-\frac{14}{9}$

$y=\frac{14}{9}x+\frac{1}{9}$

$y=- \frac{14}{9}x-\frac{1}{9}$

$y=- \frac{14}{9}x-\frac{14}{9}$

$y= \frac{1}{9}x-\frac{14}{9}$

Correct answer:

$y=- \frac{1}{9}x-\frac{14}{9}$

Explanation:

Interchange the x and y variables.

x=-9y-14

Solve for y.

Add 14 on both sides.

x+14=-9y-14+14

Simplify both sides.

x+14=-9y

Divide by negative nine on both sides.

$\frac{x+14}{-9}=\frac{-9y}{-9}$

Simplify both sides and separate the terms.

The answer is: $y=- \frac{1}{9}x-\frac{14}{9}$

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Example Question #171 : Algebraic Functions

Find the inverse of: y=2x-18

Possible Answers:

$y= \frac{1}{2}x -18$

$y=- \frac{1}{2}x +9$

$y= \frac{1}{2}x +9$

$y= \frac{1}{2}x -9$

$y= \frac{1}{2}x +18$

Correct answer:

$y= \frac{1}{2}x +9$

Explanation:

Interchange the x and y variables.

x=2y-18

Solve for y. Add 18 on both sides.

x+18=2y-18+18

Simplify both sides.

x+18=2y

Divide by 2 on both sides.

$\frac{x+18}{2}=\frac{2y}{2}$

Simplify both fractions.

The inverse function is: $y= \frac{1}{2}x +9$

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Example Question #941 : Functions And Lines

Find the inverse of y=2x+9 .

Possible Answers:

$y=\frac{1}{2}x-\frac{9}{2}$

y=-2x-9

y=-2x+9

$y=-\frac{1}{2}x+\frac{9}{2}$

$y=\frac{1}{2}x+\frac{9}{2}$

Correct answer:

$y=\frac{1}{2}x-\frac{9}{2}$

Explanation:

Interchange the x and y variables.

x=2y+9

Subtract nine from both sides.

x-9=2y+9-9

Simplify both sides.

x-9=2y

Divide by two on both sides.

$\frac{x-9}{2}=\frac{2y}{2}$

Simplify the fractions.

$\frac{1}{2}x-\frac{9}{2}=y$

The inverse is: $y=\frac{1}{2}x-\frac{9}{2}$

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Example Question #942 : Functions And Lines

The cost to go on a field trip varies inversely with the number of people attending the trip. If it costs $10 to go on the trip when 3 people are attending, how much would it cost if 15 people are attending?

Possible Answers:

$50

Correct answer:

Explanation:

Because the cost varies inversely with the number of people attending, the formula is

$C=\frac{k}{N}$

Where is the cost and is the number of people attending.

We first solve for by plugging in C=10 and N=3 .

$10=\frac{k}{3}$

$10*3=\frac{k}{3}*3$

30=k

We then evaluate when N=15

$C=\frac{30}{15}$

C=2

Therefore the cost is

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Example Question #943 : Functions And Lines

Find the inverse: y=2x+8

Possible Answers:

$y=-\frac{1}{2}x-4$

$y=\frac{1}{2}x+4$

$y=-\frac{1}{2}x+4$

$y=\frac{1}{2}x-8$

$y=\frac{1}{2}x-4$

Correct answer:

$y=\frac{1}{2}x-4$

Explanation:

Interchange the x and y variables.

x=2y+8

Solve for y. Subtract eight on both sides.

x-8=2y+8-8

x-8=2y

Divide by two on both sides.

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

Simplify both sides.

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

The answer is: $y=\frac{1}{2}x-4$

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Example Question #944 : Functions And Lines

Find the inverse of: y=9x-1

Possible Answers:

$y=\frac{1}{9}x+\frac{1}{9}$

$y=-\frac{1}{9}x+\frac{1}{9}$

y=-9x-1

$y=\frac{1}{9}x-\frac{1}{9}$

y=-9x+1

Correct answer:

$y=\frac{1}{9}x+\frac{1}{9}$

Explanation:

Interchange the x and y variables.

x=9y-1

Solve for y. Add 1 on both sides and simplify.

x+1=9y-1+1

x+1=9y

Divide by nine on both sides.

The answer is: $y=\frac{1}{9}x+\frac{1}{9}$

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Example Question #941 : Functions And Lines

Find the inverse of: f(x)= 2x-18

Possible Answers:

$y=\frac{1}{2}x -9$

$y=-\frac{1}{2}x -9$

$y=\frac{1}{2}x -18$

$y=\frac{1}{2}x +9$

$y=-\frac{1}{2}x -18$

Correct answer:

$y=\frac{1}{2}x +9$

Explanation:

Replace the f(x) term with .

y= 2x-18

Interchange the and variables.

x=2y-18

Solve for . Add on both sides.

x+18=2y-18+18

Simplify both sides.

2y=x+18

Divide by two on both sides.

$\frac{2y}{2}=\frac{x+18}{2}$

Simplify both sides.

The answer is: $y=\frac{1}{2}x +9$

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Algebra 1 : How to find inverse variation

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #935 : Functions And Lines

Example Question #4221 : Algebra 1

Example Question #171 : Algebraic Functions

Example Question #932 : Functions And Lines

Example Question #171 : Algebraic Functions

Example Question #941 : Functions And Lines

Example Question #942 : Functions And Lines

Example Question #943 : Functions And Lines

Example Question #944 : Functions And Lines

Example Question #941 : Functions And Lines

All Algebra 1 Resources

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