AlgebraHardCoefficients of a line from its intercepts
Algebra practice question
In the xy-plane, the graph of ax + by = 24 has x-intercept 6 and y-intercept −8, where a and b are constants. What is the value of a + b?
Answer: 1
At the x-intercept (6, 0): 6a = 24, so a = 4. At the y-intercept (0, −8): −8b = 24, so b = −3. Then a + b = 1.
Common wrong answers
- If you answered 7
- 7 comes from b = 3, missing the sign of the y-intercept.
- If you answered -1
- −1 reverses the signs of both.
- If you answered -2
- −2 is 6 + (−8), the sum of the intercepts, not of the coefficients.
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