A bowling alley charges its customers an hourly rate to bowl plus shoe rental. The hourly rates are per lane. A linear model of this situation contains the values (2, 34) and (3, 49.25), where x represents the number of hours bowled on one lane, and y represents the total cost for bowling. What is the rate of change in this linear model?

Answer:The rate of change for the linear model = 15.25Step-by-step explanation:Given:A linear model where [tex]x[/tex] represents number of hours bowled on one lane and [tex]y[/tex] represents the total cost of bowling.[tex](2,34)[/tex]This point shows that the cost of bowling for 2 hours = $34[tex](3,49.25)[/tex]This point shows that the cost of bowling for 3 hours = $49.25To find the rate of change in the given model we need to find the slope of the line [tex]m[/tex] using the given points.[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{49.25-34}{3-2}[/tex][tex]m=\frac{15.25}{1}[/tex][tex]m=15.25[/tex]∴ the rate of change for the linear model = 15.25This shows that the bowling alley charges its customers an hourly rate of $15.25.