Question

Franklin has a $10 bus card. Each time he rides the bus, $2 is

deducted from his card. What type of function is the
relationship between x, the number of times he uses his card
to ride the bus, and y, the number of dollars that are left on his
card?

Answer 1

The relationship between the number of times Franklin uses his card to ride the bus and the remaining balance on his card is a linear function, represented by the equation y = 10 - 2x.

Step-by-step explanation:

The relationship between x, the number of times Franklin uses his card to ride the bus, and y, the number of dollars that are left on his card is a linear function. Each time Franklin rides the bus, $2 is deducted from his card. If we let Franklin's initial amount of $10 be represented by y when x is 0 (no trips taken), we can see that every bus ride (increase in x by 1) decreases the total amount (y) by $2. This creates a straight-line graph, where y decreases at a constant rate as x increases. Therefore, the equation that represents this relationship is y = 10 - 2x, which is the standard form of a linear function where the slope is -2 and the y-intercept is 10.