Grade 9 · Algebra & functions

Linear graph translations practice

Linear graph translations is a grade 9 math skill aligned to Common Core standard HSF.BF.B.3: identify the effect on the graph of replacing f(x) by f(x) + k, k·f(x), f(kx), and f(x + k) for specific values of k. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 linear graph translations problems our math games drill.

CCSS HSF.BF.B.310 questions in the bank
Sample questions

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Question 1easy

The graph of x+3y=9x + 3y = 9 is translated up 66 units on the coordinate plane. What is the yy-coordinate of the yy-intercept of the resulting graph?

An upward shift of 66 replaces yy with y−6y - 6. At the yy-intercept, x=0x = 0, so 3(y−6)=93(y - 6) = 9. Then 3y−18=93y - 18 = 9, 3y=273y = 27, and y=9y = 9.

Question 2easy

The graph of 6x−y=186x - y = 18 is translated right 55 units on the coordinate plane. What is the xx-coordinate of the xx-intercept of the resulting graph?

A right shift of 55 replaces xx with x−5x - 5. At the xx-intercept, y=0y = 0, so 6(x−5)=186(x - 5) = 18. Then 6x−30=186x - 30 = 18, 6x=486x = 48, and x=8x = 8.

Question 3easy

The graph of 4x+2y=204x + 2y = 20 is translated down 66 units on the coordinate plane. What is the yy-coordinate of the yy-intercept of the resulting graph?

A downward shift of 66 replaces yy with y+6y + 6. At the yy-intercept, x=0x = 0, so 2(y+6)=202(y + 6) = 20. Then 2y+12=202y + 12 = 20, 2y=82y = 8, and y=4y = 4.

Question 4easy

The graph of 3x+2y=123x + 2y = 12 is translated down 33 units on the coordinate plane. What is the xx-coordinate of the xx-intercept of the resulting graph?

A downward shift of 33 replaces yy with y+3y + 3. At the xx-intercept, y=0y = 0, so 3x+2(3)=123x + 2(3) = 12. Then 3x+6=123x + 6 = 12, 3x=63x = 6, and x=2x = 2.

Question 5easy

The graph of 5x+y=255x + y = 25 is translated up 55 units on the coordinate plane. What is the yy-coordinate of the yy-intercept of the resulting graph?

An upward shift of 55 replaces yy with y−5y - 5. At the yy-intercept, x=0x = 0, so y−5=25y - 5 = 25. Then y=30y = 30.

Question 6easy

The graph of 7x−2y=147x - 2y = 14 is translated left 11 unit on the coordinate plane. What is the xx-coordinate of the xx-intercept of the resulting graph?

A left shift of 11 replaces xx with x+1x + 1. At the xx-intercept, y=0y = 0, so 7(x+1)=147(x + 1) = 14. Then 7x+7=147x + 7 = 14, 7x=77x = 7, and x=1x = 1.

Question 7medium

The graph of 2x+4y=82x + 4y = 8 is translated right 22 units on the coordinate plane. What is the yy-coordinate of the yy-intercept of the resulting graph?

A right shift of 22 replaces xx with x−2x - 2. At the yy-intercept, x=0x = 0, so 2(−2)+4y=82(-2) + 4y = 8. Then −4+4y=8-4 + 4y = 8, 4y=124y = 12, and y=3y = 3.

Question 8medium

The graph of 5x+3y=155x + 3y = 15 is translated right 33 units on the coordinate plane. What is the yy-coordinate of the yy-intercept of the resulting graph?

A right shift of 33 replaces xx with x−3x - 3. At the yy-intercept, x=0x = 0, so 5(−3)+3y=155(-3) + 3y = 15. Then −15+3y=15-15 + 3y = 15, 3y=303y = 30, and y=10y = 10.

Tests that cover linear graph translations:
SATACTPARCCNC EOG/EOCNY State Math
More Grade 9 skills:
Linear functions from tablesLinear inequalitiesLinear equation from two points (SAT)Linear inequality situationsLinear equation formsLinear inequality system solutionsLinear equation expressionsLinear system expressionsAll Grade 9 practice →

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