Question

question
sydney is going to the amusement park, where she has to pay a set price of admission and another price for tickets to go on each of the rides. the total amount of money sydney will spend is given by the equation ( y = 18 + 4x ), where ( y ) represents the total amount of money, in dollars and cents, and ( x ) represents the number of rides sydney goes on. what could the number 4 represent in the equation?
answer
the total amount of money sydney will spend if she goes on 100 rides.
the total amount of money sydney will spend if she goes on 0 rides.
the change in the total amount of money she will spend for every additional ride she goes on.
the total amount of money sydney will spend if she goes on 1 ride.
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Explanation:

Step1: Recall Slope-Intercept Form

The equation is \( y = 18 + 4x \), which is in slope - intercept form \( y=mx + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value).

Step2: Analyze the Coefficient of \( x \)

In the equation \( y = 18+4x \), the coefficient of \( x \) is 4. The variable \( x \) represents the number of rides. So, for each additional ride (increase in \( x \) by 1), the total cost \( y \) increases by 4. This means that 4 represents the change in the total amount of money she will spend for every additional ride she goes on.

Step3: Eliminate Other Options

• For the option "The total amount of money Sydney will spend if she goes on 100 rides", we would calculate \( y=18 + 4\times100=18 + 400 = 418 \), and 4 is not this total amount.
• For the option "The total amount of money Sydney will spend if she goes on 0 rides", when \( x = 0 \), \( y=18+4\times0 = 18 \), so 4 is not this amount.
• For the option "The total amount of money Sydney will spend if she goes on 1 ride", when \( x = 1 \), \( y=18 + 4\times1=22 \), and 4 is not this amount.

Answer:

The change in the total amount of money she will spend for every additional ride she goes on.