AlgebraHardEquation of a line after a vertical shift
Algebra practice question
In the xy-plane, the graph of 2x − 3y = 6 is shifted 4 units upward. Which of the following is an equation of the shifted graph?
- A. 2x − 3y = −6Correct
- B. 2x − 3y = 10
- C. 2x − 3y = 18
- D. 2x + 3y = 6
Answer: A. 2x − 3y = −6
Solve for y: y = (2/3)x − 2. Shifting up 4 gives y = (2/3)x + 2, which rearranges to 2x − 3y = −6.
Why the other answers are wrong
- B. 2x − 3y = 10
- 2x − 3y = 10 is y = (2/3)x − 10/3, a shift down.
- C. 2x − 3y = 18
- 2x − 3y = 18 is y = (2/3)x − 6, a shift down of 4.
- D. 2x + 3y = 6
- Changing the sign of 3y changes the slope, not the position.
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