AlgebraHardStandard form from slope and a point
Algebra practice question
A line in the xy-plane has slope −2 and passes through the point (1, 5). Which of the following is an equation of the line?
- A. 2x + y = 7Correct
- B. 2x − y = 7
- C. x + 2y = 11
- D. 2x + y = 3
Answer: A. 2x + y = 7
Point-slope: y − 5 = −2(x − 1), so y = −2x + 7. Rearranged: 2x + y = 7. Check: 2(1) + 5 = 7.
Why the other answers are wrong
- B. 2x − y = 7
- 2x − y = 7 has slope 2, not −2, and (1, 5) gives 2 − 5 = −3, not 7.
- C. x + 2y = 11
- x + 2y = 11 does pass through (1, 5), but its slope is −1/2, not −2.
- D. 2x + y = 3
- 2x + y = 3 has the right slope but doesn't pass through (1, 5): 2 + 5 = 7, not 3.
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