A function \(f(x)\) is linear and has a value of 29 at \(x\) = –2 and 39 at…
2015
A function \(f(x)\) is linear and has a value of 29 at \(x\) = –2 and 39 at \(x\) = 3. Find its value at \(x\) = 5.
- A.
59
- B.
45
- C.
43
- D.
35
Attempted by 44 students.
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Correct answer: C
Key insight: a linear function changes by a constant amount per unit of x.
Compute the slope (rate of change): slope = (39 - 29) / (3 - (-2)) = 10 / 5 = 2.
Find the intercept b using one known point, for example x = 3, f(3) = 39: 39 = 2×3 + b, so b = 33.
Write the linear function: f(x) = 2x + 33.
Evaluate at x = 5: f(5) = 2×5 + 33 = 10 + 33 = 43.
Therefore, the value at x = 5 is 43.