AlgebraVery hardChange in y for a change in x along a line
Algebra practice question
In the xy-plane, the points (a, 6) and (a + 3, 4) both lie on the line 2x + 3y = 10. What is the value of a?
Answer: -4
Substitute (a, 6): 2a + 18 = 10 → a = −4. Check with (a + 3, 4) = (−1, 4): −2 + 12 = 10. ✓
Common wrong answers
- If you answered 4
- 4 has the wrong sign: 2a = 10 − 18 = −8.
- If you answered -1
- −1 is a + 3, the x-coordinate of the second point.
- If you answered -8
- −8 is 2a, before dividing by 2.
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