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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #47 : Transformations Of Linear Functions

Shift the graph 2y-3x=4 down four units. What is the new equation?

Possible Answers:

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

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

$y=\frac{3}{2}x-5$

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

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

Correct answer:

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

Explanation:

Rewrite this equation in slope intercept form y=mx+b .

Add on both sides.

2y-3x+3x=4+3x

The equation becomes:

2y = 3x+4

Divide by two on both sides.

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

The equation in slope intercept form is: $y=\frac{3}{2}x+2$

Shifting this equation down four units means that the y-intercept will be decreased four units.

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

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Example Question #48 : Transformations Of Linear Functions

Shift the line x=3y+1 left three units. What is the new equation?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

Rewrite the equation x=3y+1 in slope-intercept form: y=mx+b

Subtract one from both sides.

x-1=3y+1-1

x-1=3y

Divide by three on both sides.

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

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

If this line is shifted to the left three units, replace the x-variable with (x+3) .

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

Simplify by distribution.

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

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

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Example Question #49 : Transformations Of Linear Functions

Shift the equation $y=-\frac{1}{3}x-1$ to the left two units. What is the new equation?

Possible Answers:

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

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

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

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

$y=-\frac{1}{3}x-\frac{5}{3}$

Correct answer:

$y=-\frac{1}{3}x-\frac{5}{3}$

Explanation:

If the linear function is shifted left two units, the x-variable must be replaced with the quantity of (x+2) .

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

Simplify the equation by distribution.

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

Combine like terms.

The answer is: $y=-\frac{1}{3}x-\frac{5}{3}$

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Example Question #51 : Transformations Of Linear Functions

Translate the equation y=-3x-8 left four units. What is the new equation?

Possible Answers:

y= -3x+20

y= -3x-12

y= -3x-20

y= -3x+4

y= -3x+12

Correct answer:

y= -3x-20

Explanation:

To shift the line left four units, we will need to replace the x-variable with the quantity of:

(x+4)

Replace this term in the original equation.

y=-3(x+4)-8

Use distribution to simplify.

y=-3x-12-8 = -3x-20

The answer is: y= -3x-20

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Example Question #52 : Transformations Of Linear Functions

Shift the equation y=9-9x left three units and up one unit.

Possible Answers:

y= -9x-2

y= -9x-36

y= -9x-24

y= -9x+12

y= -9x-17

Correct answer:

y= -9x-17

Explanation:

Rewrite this equation in slope-intercept form, y=mx+b .

y=-9x+9

Shifting this equation up one unit will add one to the y-intercept.

y=-9x+9+(1) = -9x+10

The equation becomes: y= -9x+10

To shift this equation left three units, we will need to replace the x-variable with the quantity (x+3) .

y= -9(x+3)+10

Use distribution to simplify the equation.

y= -9x-27+10 = -9x-17

The answer is: y= -9x-17

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Example Question #53 : Transformations Of Linear Functions

The line y=3x-29 is shifted right 5 units. What must be the new equation?

Possible Answers:

y= 3x-44

y= 3x-34

$\textup{The answer is not given.}$

y= 3x-24

y= 3x-14

Correct answer:

y= 3x-44

Explanation:

If the line is shifted right 5 units, we will need to replace the x-variable of the equation with the quantity (x-5) .

y=3(x-5)-29

Simplify by distribution.

y=3x-15-29 = 3x-44

The answer is: y= 3x-44

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Example Question #54 : Transformations Of Linear Functions

Shift the equation x+9y=3x+2 up two units. What is the new equation?

Possible Answers:

$y=\frac{2}{9}x+\frac{8}{9}$

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

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

$y=\frac{2}{9}x+\frac{20}{9}$

$y=\frac{2}{9}x+\frac{28}{9}$

Correct answer:

$y=\frac{2}{9}x+\frac{20}{9}$

Explanation:

Before we apply any transformations, we will need to put the equation in slope-intercept form, y=mx+b .

Subtract from both sides.

x+9y-x=3x+2-x

9y=2x+2

Divide by nine on both sides.

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

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

Shifting the equation up two units will add 2, or $\frac{18}{9}$ to the y-intercept.

$y=\frac{2}{9}x+\frac{2}{9}+\frac{18}{9}$

The answer is: $y=\frac{2}{9}x+\frac{20}{9}$

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Example Question #55 : Transformations Of Linear Functions

Shift the line y=-4x-8 to the left 8 units. What is the new equation?

Possible Answers:

y=-4x+32

y=-4x-32

y=-4x-16

y=-4x+16

y=-4x-40

Correct answer:

y=-4x-40

Explanation:

To shift the line left 8 units, we will need to replace the x-value with (x+8) .

y=-4(x+8)-8

Distribute the negative four through the binomial.

y=-4x-32 -8

Combine like-terms.

The answer is: y=-4x-40

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Example Question #56 : Transformations Of Linear Functions

Shift the equation y=-9x-5 left eight units. What must be the new equation?

Possible Answers:

y=-9x-3

y=-9x-77

y=-9x-67

y=-9x+77

y=-9x-13

Correct answer:

y=-9x-77

Explanation:

To shift the equation left eight units, replace the x-variable with the quantity of (x+8) .

y=-9(x+8)-5

Simplify this equation.

y=-9x-72-5

Combine like-terms.

The answer is: y=-9x-77

Report an Error

Example Question #57 : Transformations Of Linear Functions

If the equation x+y=9 is shifted left 9 units, what is the equation after the translation?

Possible Answers:

y=-x+18

y=x

y=-x

y=x+18

y=-x-18

Correct answer:

y=-x

Explanation:

Rewrite the given line in standard form to slope-intercept format:

y=mx+b

Subtract on both sides.

x+y-x=9-x

y=-x+9

Replace the x-value with the quantity of (x+9) since we are shifting the equation left 9 units.

y=-(x+9)+9

Distribute the negative sign through both terms of the binomial.

y=-x-9+9

The answer is: y=-x

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #47 : Transformations Of Linear Functions

Example Question #48 : Transformations Of Linear Functions

Example Question #49 : Transformations Of Linear Functions

Example Question #51 : Transformations Of Linear Functions

Example Question #52 : Transformations Of Linear Functions

Example Question #53 : Transformations Of Linear Functions

Example Question #54 : Transformations Of Linear Functions

Example Question #55 : Transformations Of Linear Functions

Example Question #56 : Transformations Of Linear Functions

Example Question #57 : Transformations Of Linear Functions

All Algebra II Resources

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