You bought a pre-paid metro card for $50. Every time you ride the metro it deducts $1.50 from your card. How much money is on your card after 1 trip, 2 trips, 3 trips, 13 trips, and X trips?

Question

What is the rate of change:

Where does the rate of change show upin the context, the table, the graph and the algebraic expression?

How do you know that the function is linear?

Answer 1

X	1.5X	Remaining ($)
1	1.5	48.50
2	3	47.00
3	4.5	45.50
13	19.5	30.50
X	1.5X	50-1.5X

The table shows in the middle column the result of multiplying the number of trips by the cost of a trip.

After X trips the money remaining is 50-1.5X, so:

X remaining $

1 48.50

2 47

3 45.50

13 50-19.50=30.50

Let y=50-1.5X. The rate of change is -1.5 (the slope). This shows in the amount deducted per trip. In the graph it is the gradient or slope of the line (\). In the algebraic expression it is the coefficient of X.

We know it's linear because the graph is a straight line.