AlgebraEasy–MediumIntercepts from standard form
Algebra practice question
In the xy-plane, the line 2x + 3y = 6 crosses the x-axis at (a, 0) and the y-axis at (0, b). What are the values of a and b?
- A. a = 3, b = 2Correct
- B. a = 2, b = 3
- C. a = 6, b = 6
- D. a = −3, b = −2
Answer: A. a = 3, b = 2
x-intercept: set y = 0, 2x = 6, x = 3. y-intercept: set x = 0, 3y = 6, y = 2. So a = 3 and b = 2.
Why the other answers are wrong
- B. a = 2, b = 3
- The intercepts are swapped; a is where y = 0, giving 2x = 6, x = 3.
- C. a = 6, b = 6
- 6 is the constant, but each intercept divides it by the other variable's coefficient.
- D. a = −3, b = −2
- Both intercepts are positive here: 2(3) = 6 and 3(2) = 6.
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