AlgebraVery hardCoefficients from the intercepts
Algebra practice question
In the xy-plane, the line ax + by = 12, where a and b are constants, has an x-intercept of 4 and a y-intercept of −6. What is the value of a + b?
Answer: 1
At (4, 0): 4a = 12, so a = 3. At (0, −6): −6b = 12, so b = −2. Then a + b = 3 + (−2) = 1.
Common wrong answers
- If you answered 3
- 3 is a alone; add b = −2.
- If you answered 5
- 5 uses b = 2, missing the sign: −6b = 12 gives b = −2.
- If you answered -2
- −2 is b alone; add a = 3.
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