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Algebra II : Transformations of Linear Functions

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Example Question #90 : Linear Functions

Shift the graph: y=2(2x+3) up five units. What is the new equation?

Possible Answers:

y =4x+11

y =4x+8

y =4x+10

y =4x+18

y =4x+15

Correct answer:

y =4x+11

Explanation:

Use distribution to simplify this equation. We will need to put the equation in slope-intercept format, y=mx+b

y=2(2x+3) =2(2x)+2(3) =4x+6

The equation becomes: y =4x+6

Shifting this equation up five units will add five to the y-intercept.

The answer is: y =4x+11

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Example Question #41 : Transformations Of Linear Functions

Shift the graph $y=9-\frac{2}{9}x$ three units to the left. What's the new equation?

Possible Answers:

$y=-\frac{2}{9}x+\frac{25}{3}$

$y=-\frac{2}{9}x+3$

$y=-\frac{2}{9}x+\frac{1}{6}$

$y=-\frac{2}{9}x+\frac{31}{3}$

$y=-\frac{2}{9}x+\frac{29}{3}$

Correct answer:

$y=-\frac{2}{9}x+\frac{25}{3}$

Explanation:

In order to shift an equation to the left three units, the x-variable will need to be replaced with the quantity of (x+3) . This shifts all points left three units.

$y=9-\frac{2}{9}(x+3)$

Simplify the equation.

$y=9-\frac{2}{9}x-\frac{2}{3} = \frac{27}{3}-\frac{2}{9}x-\frac{2}{3}$

The answer is: $y=-\frac{2}{9}x+\frac{25}{3}$

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Example Question #42 : Transformations Of Linear Functions

Shift the line y=9(2x-1) up six units. What is the new equation?

Possible Answers:

y= 18x+6

y= 18x+11

y= 18x-3

y= 18x-8

y= 18x-15

Correct answer:

y= 18x-3

Explanation:

Add six to the equation since a vertical shift will increase the y-intercept by six units.

y=9(2x-1)+6

Simplify this equation by distribution.

y=9(2x)-9(1)+6 = 18x-3

The answer is: y= 18x-3

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Example Question #43 : Transformations Of Linear Functions

Translate the function: 3y=4-x to the left 5 units. What is the equation in slope-intercept format?

Possible Answers:

$y= -\frac{1}{3}x+\frac{8}{3}$

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

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

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

$y= -\frac{1}{3}x-\frac{8}{3}$

Correct answer:

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

Explanation:

Divide by three on both sides.

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

The equation becomes: $y=-\frac{1}{3}x+\frac{4}{3}$

If this equation shifts to the left five units, we will need to replace the x term with the quantity (x+5) .

$y=-\frac{1}{3}(x+5)+\frac{4}{3}$

Simplify this equation by distribution.

$y=-\frac{1}{3}(x+5)+\frac{4}{3} = -\frac{1}{3}x-\frac{5}{3}+\frac{4}{3}$

Combine like-terms.

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

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Example Question #44 : Transformations Of Linear Functions

Translate the function y=3x-15 to the left four units. What is the new equation?

Possible Answers:

y=3x-6

y=3x-12

y=3x+3

y=3x-8

y=3x-3

Correct answer:

y=3x-3

Explanation:

Translation of a graph to the left four units will require replacing the x-variable with the quantity:

(x+4)

Replace the term inside the equation.

y=3(x+4)-15

Use distribution so simplify the terms.

y=3x+12-15

Simplify the equation.

The answer is: y=3x-3

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Example Question #45 : Transformations Of Linear Functions

Shift the equation x+3y=17 up two units. What is the new equation?

Possible Answers:

$y=-\frac{1}{3}x-14$

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

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

$y= -\frac{1}{3}x-8$

$y= -\frac{1}{3}x+\frac{23}{3}$

Correct answer:

$y= -\frac{1}{3}x+\frac{23}{3}$

Explanation:

In order to find the equation after the translation, we will need to put the equation in slope-intercept format, y=mx+b .

Subtract from both sides of the equation.

x+3y-x=17-x

The equation becomes: 3y= -x+17

Divide by three on both sides.

$\frac{3y}{3}= \frac{-x+17}{3}$

$y=-\frac{1}{3}x +\frac{17}{3}$

Add two to the y-intercept for the vertical shift. This is the same as adding $\frac{6}{3}$ .

$y=-\frac{1}{3}x +\frac{17}{3}+\frac{6}{3} = -\frac{1}{3}x+\frac{23}{3}$

The equation is: $y= -\frac{1}{3}x+\frac{23}{3}$

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Example Question #46 : Transformations Of Linear Functions

If the graph x+y=-9 is translated 5 units left, what is the new equation?

Possible Answers:

y=-x+5

y=-x+14

y=-x-5

y=-x-14

y=-x+19

Correct answer:

y=-x-14

Explanation:

Rewrite the given equation in standard form to slope intercept format, y=mx+b .

Subtract x from both sides.

x+y-x=-9-x

The slope intercept form is: y=-x-9

If the line is translated 5 units to the left, we need to replace the quantity of x with (x+5) .

y=-(x+5)-9

Simplify the equation. Distribute the negative through the binomial.

y=-(x+5)-9 = -x-5-9 =-x-14

The answer is: y=-x-14

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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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Algebra II : Transformations of Linear Functions

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #90 : Linear Functions

Example Question #41 : Transformations Of Linear Functions

Example Question #42 : Transformations Of Linear Functions

Example Question #43 : Transformations Of Linear Functions

Example Question #44 : Transformations Of Linear Functions

Example Question #45 : Transformations Of Linear Functions

Example Question #46 : Transformations Of Linear Functions

Example Question #47 : Transformations Of Linear Functions

Example Question #48 : Transformations Of Linear Functions

Example Question #49 : Transformations Of Linear Functions

All Algebra II Resources

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