Which option has (y) increasing by (6) each time (x) increases and (y(0)=14)?

Correct answer: \(y=14+6x\)

In the linear form \(y=b+mx\), \(b=y(0)\), while \(m\) gives the change in \(y\) when \(x\) increases by 1. Here, \(y(0)=14\), so the constant term is 14; and \(y\) increases by 6 each time, so the coefficient is 6. Therefore, \(y=14+6x\) is correct. In \(y=6+14x\), the growth rate is 14, while \(y=14-6x\) represents a decrease of 6. Exam tip: substitute \(x=0\) to check the initial value, then check the coefficient of \(x\).