Question

The line \(y = mx\) bisects the area enclosed by lines \(x = 0\), \(y = 0\), and \(x = \frac{3}{2}\) and the curve \(y = 1 + 4x - x^2\). Then, the value of \(m\) is:

• A. \( \frac{13}{6} \)
• B. \( \frac{13}{2} \)
• C. \( \frac{13}{5} \)
• D. \( \frac{13}{7} \)

Hint:

To solve area bisecting problems, equate the area under the line to half of the total area, then solve for the unknown slope.