Equation for linear relationship is y=mx+b, where m is slope (rate of change), and b is y-intercept. Y-intercept is where you start of at. Like if I had 20 dollars and started earning 5 dollars each day, my y-intercept would be 20 dollars.
Your rate of change is $5 dollars PER HOUR, and y-intercept is $15 dollars. this is because it is a flat fee. She could walkyour dog for 5 minutes but she still charges 15 dollars.