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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #77 : Linear Functions

Shift y=6x up two units and left two units. What is the new equation?

Possible Answers:

y=6x-14

y=6x-10

y=6x+8

y=6x+14

y=6x-4

Correct answer:

y=6x+14

Explanation:

Apply the vertical transformation. Shifting up two units will add two to the y-intercept.

y=6x+2

Shifting the graph two units to the left will require a replacement of the x-variable with (x+2) .

y=6(x+2)+2

Simplify this equation.

y=6x+12+2= 6x+14

The answer is: y=6x+14

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Example Question #78 : Linear Functions

Shift the equation y=6x-30 right four units. What's the new equation?

Possible Answers:

y= 6x-54

y= 6x+34

y=6x+54

y= 6x-26

y= 6x-41

Correct answer:

y= 6x-54

Explanation:

A translation to the right four units will require the x-variable to be replaced with (x-4) .

Rewrite the equation.

y=6(x-4)-30

Simplify the binomial by distribution.

y=6x-24-30 = 6x-54

The answer is: y= 6x-54

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Example Question #79 : Linear Functions

Shift the equation y= 8x-3 left five units. What is the new equation?

Possible Answers:

y= 8x-32

y= 8x-16

y= 8x-12

y= 8x+37

y= 8x-37

Correct answer:

y= 8x+37

Explanation:

If a linear function is shifted left five units, the x-variable will need to be replaced with (x+5) . Replace the term, and simplify the equation.

y= 8(x+5)-3

Distribute the eight through both terms of the binomial.

y= 8x+40-3 = 8x+37

The answer is: y= 8x+37

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Example Question #31 : Transformations Of Linear Functions

Shift the equation y=9-x up three units and left six units. What is the new equation?

Possible Answers:

y= -x-18

y= -x+6

y= -x+18

y= -x-6

y= -x-12

Correct answer:

y= -x+6

Explanation:

Rewrite the equation in slope intercept form.

y=-x+9

Shifting the graph up by three units will require adding three to the y-intercept.

y=-x+9=-x+9+(3) = -x+12

Shifting the graph left six units mean that the x-variable will need to be replaced with: (x+6)

The equation becomes:

y=-(x+6)+12

Simplify this equation.

y=-x-6+12 = -x+6

The answer is: y= -x+6

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Example Question #31 : Transformations Of Linear Functions

Shift the graph 2x+3y = 6 down six units. What is the new equation?

Possible Answers:

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

$y=-\frac{2}{3}x-16$

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

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

$y=-\frac{2}{3}x-8$

Correct answer:

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

Explanation:

Rewrite the given equation in standard form to slope-intercept form.

y=mx+b

Subtract from both sides.

2x+3y -2x= 6-2x

3y=-2x+6

Divide by three on both sides.

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

Simplify this equation.

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

Shifting this equation down means that the y-intercept will be subtracted six.

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

The answer is: $y=-\frac{2}{3}x-4$

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Example Question #82 : Linear Functions

Translate the graph y=10-2x down fifteen units. What is the new equation?

Possible Answers:

y=-2x-5

y=-13x+10

y=-2x-25

y=-2x+25

y=-2x+5

Correct answer:

y=-2x-5

Explanation:

The given equation can be rewritten in slope-intercept format, y=mx+b .

$y=10-2x \rightarrow y=-2x+10$

Shifting down a line fifteen units will decrease the y-intercept by 15.

y=-2x+10-15

The answer is: y=-2x-5

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Example Question #83 : Linear Functions

Translate the graph y=2x+5 left four units and up one unit. What's the new equation?

Possible Answers:

y= 2x-17

y= 2x-3

y= 2x-7

y= 2x+14

y= 2x+8

Correct answer:

y= 2x+14

Explanation:

Shifting the equation up one unit will change the y-intercept by adding one.

y=2x+5+(1) = 2x+6

If the graph is to be shifted four units to the left, the x-variable will need to be replaced with the quantity (x+4) .

y=2(x+4)+6

Use the distribution property to simplify the binomial.

y=2x+8+6 = 2x+14

The equation is: y= 2x+14

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Example Question #84 : Linear Functions

Shift the function x+3y=6 up four units. What is the new equation?

Possible Answers:

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

$y=-\frac{1}{3}x+\frac{16}{3}$

$y=-3x+\frac{16}{3}$

$y=-\frac{1}{3}x+\frac{3}{10}$

y=-3x+6

Correct answer:

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

Explanation:

Rewrite this equation in standard form to slope intercept format.

Subtract on both sides.

x+3y-x=6-x

3y=-x+6

Divide by three on both sides.

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

Simplify this equation.

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

If this graph is shifted up four units, simply add four to the y-intercept.

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

The answer is: $y=-\frac{1}{3}x+6$

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Example Question #85 : Linear Functions

Shift y=6x-4 left eight units. What is the new equation?

Possible Answers:

y= 6x-52

y= 6x+12

y= 6x+44

y= -2x+44

y= 6x-36

Correct answer:

y= 6x+44

Explanation:

Shifting the graph left 8 units will require changing the x-variable to (x+8) .

Replace the term and simplify the equation.

y=6(x+8)-4

Distribute the six through the binomial.

y=6x+48-4 = 6x+44

The equation is: y= 6x+44

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Example Question #86 : Linear Functions

Translate the function y=3-9x left 5 units. What is the new equation?

Possible Answers:

y=-9x+46

y=-9x-42

y=-9x-15

y=-9x-62

y=-9x+18

Correct answer:

y=-9x-42

Explanation:

If the graph is shifted leftward, apply the transformation by replacing the x-variable with (x+5) .

y=3-9(x+5)

Simplify this equation by distribution, and rewrite this in slope intercept format.

y=3-9x-45

Combine like-terms.

The answer is: y=-9x-42

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #77 : Linear Functions

Example Question #78 : Linear Functions

Example Question #79 : Linear Functions

Example Question #31 : Transformations Of Linear Functions

Example Question #31 : Transformations Of Linear Functions

Example Question #82 : Linear Functions

Example Question #83 : Linear Functions

Example Question #84 : Linear Functions

Example Question #85 : Linear Functions

Example Question #86 : Linear Functions

All Algebra II Resources

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