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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 #67 : Linear Functions

Shift the line y=3x+9 up two units and left three units. What's the new equation?

Possible Answers:

y=3x+11

y=3x+2

y=3x+14

y=3x+8

y=3x+20

Correct answer:

y=3x+20

Explanation:

Shifting the line up two units will add two to the y-intercept.

y=3x+9+(2) =3x+11

Shifting the line left three units mean that the x-variable will be replaced with:

x+3

Replace with the quantity of x+3 .

y=3(x+3)+11 = 3x+9+11

Simplify this equation by combining like-terms

The answer is: y=3x+20

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Example Question #15 : Transformations Of Linear Functions

Shift the line y=2(2x-5) left 2 units. Write the new equation.

Possible Answers:

y= 4x+16

y= 4x+8

y= 4x-8

y= 4x-2

y= 4x-16

Correct answer:

y= 4x-2

Explanation:

Expand the equation by distribution.

y=2(2x-5) = 4x-10

Since this line is shifted left two units, replace the variable with x+2 .

The equation becomes:

y=4(x+2)-10 = 4x+8-10 = 4x-2

The new equation after the shift is: y= 4x-2

The answer is: y= 4x-2

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Example Question #11 : Transformations Of Linear Functions

Determine the new equation if y=9x-10 is shifted ten units to the left.

Possible Answers:

y=9x+70

y=9x-20

y=9x

y=9x-2

y=9x+80

Correct answer:

y=9x+80

Explanation:

If a line is shifted ten units to the left, the x-variable will be replaced with (x+10) since the root will be ten units to the left of the original location.

The equation becomes:

y=9(x+10)-10

Simplify the linear equation.

y= 9x+90-10

The answer is: y=9x+80

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Example Question #21 : Transformations Of Linear Functions

Shift the function y=-2x+50 right five units. What's the new equation?

Possible Answers:

y= -2x+45

y= -2x-250

y= -2x+60

y= -2x-60

y= -2x+250

Correct answer:

y= -2x+60

Explanation:

Shifting the line right five units will shift the root right by five units.

This means that the variable will need to be replaced with (x-5) since all of the x-values are shifted right five units.

The new equation becomes: y=-2(x-5)+50

Simplify the equation.

y=-2x+10+50= -2x+60

The answer is: y= -2x+60

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Example Question #882 : Algebra Ii

Shift the line: y=3x-1 up two units and left five units. What is the new equation?

Possible Answers:

y =3x-5

y =3x+2

y =3x+6

y =3x+16

y =3x-14

Correct answer:

y =3x+16

Explanation:

Shifting the line up two units will add two to the y-intercept.

y=3x-1+(2) = 3x+1

Shifting the line left five units will indicate that the x-variable will be changed to:

x+5

Replace this quantity into the equation.

y=3(x+5)+1

Simplify this equation.

y=3x+15+1 =3x+16

The answer is: y =3x+16

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Example Question #72 : Linear Functions

Shift the equation 2x+y=9 left eight units. What's the new equation?

Possible Answers:

y=-2x-7

y=-2x+7

y=-2x-50

y=2x-7

y=-2x-25

Correct answer:

y=-2x-7

Explanation:

If a function is shifted left eight units, we will need to replace the term with the quantity (x+8) .

2(x+8)+y=9

Use the distributive property to simplify the binomial.

2x+16+y=9

Solve for y. Subtract and on both sides.

2x+16+y-[2x]-(16)=9-[2x]-(16)

Simplify both sides.

The answer is: y=-2x-7

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Example Question #21 : Transformations Of Linear Functions

Translate the following function left three units: y=9-6x Write the new equation.

Possible Answers:

y=-6x-9

y=-6x+6

y=-6x+27

y=-6x-27

y=-6x+12

Correct answer:

y=-6x-9

Explanation:

When the graph is shifted three units to the left, the x-variable of the equation will need to be replaced with (x+3) .

Replace the x term with the new term.

y=9-6(x+3)

Simplify this equation.

y=9-6x-18

Combine like-terms.

The answer is: y=-6x-9

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Example Question #884 : Algebra Ii

Translate x+6y=-5 down two units. What's the new equation?

Possible Answers:

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

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

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

$y=-\frac{1}{6}x-\frac{7}{6}$

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

Correct answer:

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

Explanation:

Rewrite the equation, x+6y=-5 , in slope intercept form.

y=mx+b

Subtract on both sides.

x+6y-x=-5-x

6y = -x-5

Divide by six on both sides.

$\frac{6y }{6}= \frac{-x-5}{6}$

Simplify both sides.

The equation in slope intercept form is: $y=-\frac{1}{6}x-\frac{5}{6}$

Shifting the function down by two units mean that the y-intercept will be subtracted by two.

$y=-\frac{1}{6}x-\frac{5}{6}-(2) = -\frac{1}{6}x-\frac{5}{6}-(\frac{12}{6})$

The answer is: $y=-\frac{1}{6}x-\frac{17}{6}$

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Example Question #361 : Functions And Graphs

Shift the equation y=-5x+6 left five units. What is the new equation?

Possible Answers:

y=-5x+19

y=-5x-19

y=-5x+35

y=-5x-11

y=-5x+1

Correct answer:

y=-5x-19

Explanation:

The graph translated five units to the left will require the x-variable to be replaced with (x+5) .

Replace the term.

y=-5(x+5)+6

Simplify by distribution.

y=-5(x+5)+6 = -5x-25+6

The equation of the new line is: y=-5x-19

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Example Question #76 : Linear Functions

Shift x-y = -1 down four units. Determine the new equation.

Possible Answers:

y=x-4

y=x-3

y=-x+3

y=x+3

y=-x-4

Correct answer:

y=x-3

Explanation:

Convert the equation in standard form to slope-intercept form, y=mx+b .

Add on both sides.

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

x=y-1

Add one on both sides.

x+1=y-1+1

The equation becomes: x+1=y

Shifting this equation down four units means that the y-intercept must be subtracted four units.

x+1-4=y

The answer is: y=x-3

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #67 : Linear Functions

Example Question #15 : Transformations Of Linear Functions

Example Question #11 : Transformations Of Linear Functions

Example Question #21 : Transformations Of Linear Functions

Example Question #882 : Algebra Ii

Example Question #72 : Linear Functions

Example Question #21 : Transformations Of Linear Functions

Example Question #884 : Algebra Ii

Example Question #361 : Functions And Graphs

Example Question #76 : Linear Functions

All Algebra II Resources

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