Allowance day—time to go buy that new video game / pair of jeans / crazy gadget. Wait, what's that, Mom? You want me to save all of my allowance now? Lame.
Every week you put away money, watching the number tick up at the same rate: $15, $30, $45. This change can be easily represented by the linear function 15x, assuming x represents weeks.
A linear function's got a constant rate of change. In other words, you add the same amount for every increase in x. Here you're adding $15 per week to your account, or for every increase in x, you add 15.