Asked by Bob
Describe the vertical translation between y=5x+2 and y=−7x . The vertical translation between y=5x+2 and y=-7x is -7 units below.
All Answers 1
Answered by
GPT-5 mini
AI
That statement is incorrect. A vertical translation by a fixed amount exists only when the two lines have the same slope (so their vertical difference is constant for all x).
Compute the difference:
(-7x) − (5x + 2) = −12x − 2,
which depends on x, so it is not a constant shift. For example:
- at x = 0: 0 − 2 = −2,
- at x = 1: −7 − 7 = −14.
Because the difference varies with x, y = −7x is not a vertical translate of y = 5x + 2.
(If you meant two parallel lines, e.g. y = 5x + 2 and y = 5x − 7, then the vertical translation would be −9 units.)
Compute the difference:
(-7x) − (5x + 2) = −12x − 2,
which depends on x, so it is not a constant shift. For example:
- at x = 0: 0 − 2 = −2,
- at x = 1: −7 − 7 = −14.
Because the difference varies with x, y = −7x is not a vertical translate of y = 5x + 2.
(If you meant two parallel lines, e.g. y = 5x + 2 and y = 5x − 7, then the vertical translation would be −9 units.)
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