Four friends went to a festival, where they each had to pay an entrance fee and buy tickets for each ride they went on.
The table below shows how much money each of them spent at the festival and the number of rides each went on.Find the rate of change between each of the friends.
Make sure to write each rate of change as a unit rate.
Individual Number of rides Amount of Money Spent
Friend 1. 4. 10.5
Friend 2. 7. 15.75
Friend 3. 3. 8.75
Friend 4. 6. 14.
f.) If the table of values represents a linear function, write the equation of the linear function: y=.
(1 point)
g.) Rate of change in the equation:
h.) What does this rate mean in the context? (1 point)
1.) Initial value in the equation:
¡.) What does the initial value mean in the context? (1 point
First, let's calculate the rate of change (slope) between each of the friends:
Between Friend 1 and Friend 2:
Rate of change = (15.75 - 10.5) / (7 - 4) = 5.25 / 3 = 1.75
Between Friend 2 and Friend 3:
Rate of change = (8.75 - 15.75) / (3 - 7) = -7 / -4 = 1.75
Between Friend 3 and Friend 4:
Rate of change = (14 - 8.75) / (6 - 3) = 5.25 / 3 = 1.75
Therefore, the rate of change between each of the friends is 1.75. This can be written as a unit rate by dividing the rate of change by 1, so the unit rate of change is 1.75.
f.) Since the rate of change between each friend is 1.75, it indicates that there is a constant rate of change. This suggests that the table of values represents a linear function.
To write the equation of the linear function, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Let's choose Friend 1's values as our reference point: (4, 10.5)
The equation of the linear function is:
y - 10.5 = 1.75(x - 4)
Simplifying the equation gives:
y - 10.5 = 1.75x - 7
y = 1.75x + 3.5
Therefore, the equation of the linear function is y = 1.75x + 3.5.
g.) The rate of change in the equation is the coefficient of x, which is 1.75.
h.) This rate of change represents the amount of money spent for each additional ride, which is $1.75.
1.) The initial value in the equation is the y-intercept, which is 3.5.
¡.) The initial value represents the amount of money spent when no rides were taken, which is $3.5.