Question

12 devon uses the equation $c = 9.75t$ to determine the total cost in dollars, $c$, for $t$ tickets to the fair. decide if each statement about the equation is true or false. choose true or false for each statement. a. the equation $c = 9.75t$ represents a proportional relationship. b. for every 9.75 tickets, devon pays $1. c. the constant of proportionality is 9.75. d. for each ticket, devon pays $9.75.

Explanation:

Step1: Analyze Statement a

A proportional relationship has the form \( y = kx \) (where \( k \) is a constant), and \( c = 9.75t \) fits this form (with \( k = 9.75 \), \( y = c \), \( x = t \)). So it is proportional. So statement a is True.

Step2: Analyze Statement b

The equation \( c = 9.75t \) means for \( t \) tickets, cost is \( 9.75t \). So for 1 ticket (\( t = 1 \)), \( c = 9.75 \), not for 9.75 tickets costing $1. So statement b is False.

Step3: Analyze Statement c

In \( y = kx \), \( k \) is the constant of proportionality. Here \( c = 9.75t \), so \( k = 9.75 \). So statement c is True.

Step4: Analyze Statement d

When \( t = 1 \) (1 ticket), \( c = 9.75\times1 = 9.75 \). So each ticket costs $9.75. Statement d is True.

Answer:

a. True
b. False
c. True
d. True