Question

1. FUNDRAISING The Pep Club rented a shaved ice machine to sell shaved ice as a fundraiser. They paid an initial fee and then an hourly charge. The table shows the cost per hour. Find and interpret the rate of change and initial value. Assume the relationship between the two quantities is linear. Number of Hours, 3 2 1A Cost ($), y 30 40 45

Answer 1

First, find the slope (m)

`m=(y2-y1)/(x2-x1)`

Use 2 points from the table:

(x1,y1) = (2,30)

(x2,y2) = (3,35)

Replace;

`m=(35-30)/(3-2)=(5)/(1)=5`

slope = rate of change = cost per hour

to find the initial value, apply the slope intercept equation:

y= mx+b

where:

m= slope

b= inital value

replace (x,y) by a point from the table and solve for b

30 = 5(2) +b

30=10 +b

30-10= b

b=20

inital value = 20