In the line \(y=-\frac{7}{4}x+18\), how much should (x) increase to decrease (y) by (42)?

Correct answer: 24

The slope is \(-\frac{7}{4}\). Thus, when \(x\) increases by 4 units, \(y\) decreases by 7 units. For a decrease of 42 in \(y\), \(\frac{7}{4}\Delta x=42\). Hence \(\Delta x=42\times\frac{4}{7}=24\). If 28 were chosen, the decrease in \(y\) would be \(\frac{7}{4}\times 28=49\), not 42. Exam tip: In change-based questions, use the slope; the constant term 18 does not affect the change.