In the line \(y=\frac{7}{5}x-12\), how much should (x) increase to increase (y) by (28)?

Correct answer: 20

The slope is \(\frac{7}{5}\), so an increase of 5 in \(x\) produces an increase of 7 in \(y\). Hence, \(\Delta y=\frac{7}{5}\Delta x\). Putting \(\Delta y=28\), we get \(28=\frac{7}{5}\Delta x\), so \(\Delta x=28\times\frac{5}{7}=20\). Therefore, 20 is correct. If \(x\) increased by 25, \(y\) would increase by 35, not 28. Exam tip: For a linear equation \(y=mx+c\), use \(\Delta y=m\Delta x\) to compare changes.