AlgebraMediumIdentifying the graph feature from the equation
Algebra practice question
The function f is defined by f(x) = −(3/4)x + 6. Which statement about the graph of y = f(x) in the xy-plane is true?
- A. It crosses the y-axis at 6 and the x-axis at 8.Correct
- B. It crosses the y-axis at 6 and the x-axis at −8.
- C. It crosses the y-axis at −3/4 and the x-axis at 6.
- D. It crosses the y-axis at 8 and the x-axis at 6.
Answer: A. It crosses the y-axis at 6 and the x-axis at 8.
f(0) = 6. Setting f(x) = 0: (3/4)x = 6, x = 8.
Why the other answers are wrong
- B. It crosses the y-axis at 6 and the x-axis at −8.
- The x-intercept is positive: −(3/4)x + 6 = 0 gives x = 8.
- C. It crosses the y-axis at −3/4 and the x-axis at 6.
- −3/4 is the slope, not an intercept.
- D. It crosses the y-axis at 8 and the x-axis at 6.
- The intercepts are swapped.
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