In the line \(y=\frac{9}{4}x-15\), how much should (x) increase to increase (y) by (36)?

Correct answer: 16

The slope is \(\frac{9}{4}\), so an increase \(\Delta x\) in \(x\) produces an increase \(\frac{9}{4}\Delta x\) in \(y\). Thus, \(\frac{9}{4}\Delta x=36\), giving \(\Delta x=36\times\frac{4}{9}=16\). If \(x\) increased by 18, then \(y\) would increase by \(\frac{9}{4}\times18=40.5\), not 36. Exam tip: for change questions in \(y=mx+c\), use \(\Delta y=m\Delta x\); the constant term \(c\) does not affect the change.