Question

Holly, Maria and Johnny went to a fair over Spring Break. Holly paid $12.50 and went on one ride. Maria paid $15.00 and went on two rides. Johnny paid $20.00 and went on 4 rides. With x being the number of rides and y being the total amount paid, is the situation linear and why?

No. Between Holly and Maria there is an increase of $2.50 and between Maria and Johnny there is an increase of $5.00.

Yes. The y-intercept can be determined to be $10.00.

Yes. There is a constant rate of increase of $2.50 for each ride.

No. We are not given the initial cost if they went on no rides.

Answer 1

Yes. There is a constant rate of increase of $2.50 for each ride.

Explanation:

Lets write each persons cost and rides in the form y =mx+b

y being the total cost and x is the number of rides

Holly

(1 , 12.50)

Maria

(2,15)

Johnny

(4,20)

Lets calculate the slope

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

= (20-15)/ (4-2)

= 5/2

We can use the point slope form to determine b

y-y1 = m(x-x1)

y-20 = 5/2 (x-4)

Distribute

y-20 = 5/2x -20/2

Add 20 to each side

y-20+20 = 5/2x -10 +20

y = 5/2x +10

The slope or cost per ride is 2.50 and the y intercept is 10