If (y=(k+6)x+1) increases (y) by (52) when (x) increases by (4), what is (k)?

Correct answer: \(7\)

In this linear equation, the rate of change of \(y\) with respect to \(x\), or slope, is \(k+6\). Using \(\Delta y=(k+6)\Delta x\), we get \(52=(k+6)\times4\). Hence \(k+6=13\), so \(k=7\). If \(k=6\), the slope would be \(12\), giving an increase of only \(48\) in \(y\) for an increase of \(4\) in \(x\). Exam tip: the constant term \(+1\) does not affect the change in \(y\).