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 I. 4. 10.5
Friend 2. 7. 15.75
Friend 3. 3. 8.75
Friend 4. 6. 14.
a.) Rate of change between Friend 1 and Friend 2: __
b.) Rate of change between Friend 2 and Friend 3: ___
c.) Rate of change between Friend 3 and Friend 4:___
d. Does this table show a linear relationship? (1 point)
o Yes
O No
e.) Explain why or why not this is a linear relationship. (1 point)
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:____
j.) What does the initial value mean in the context? (1 point)
a.) Rate of change between Friend 1 and Friend 2: The rate of change can be found by finding the difference in the amount of money spent and dividing it by the difference in the number of rides. Therefore,
Rate of change = (15.75 - 10.5) / (7 - 4)
= 5.25 / 3
= 1.75
So, the rate of change between Friend 1 and Friend 2 is 1.75.
b.) Rate of change between Friend 2 and Friend 3: Similarly,
Rate of change = (8.75 - 15.75) / (3 - 7)
= -7 / -4
= 1.75
So, the rate of change between Friend 2 and Friend 3 is 1.75.
c.) Rate of change between Friend 3 and Friend 4: Similarly,
Rate of change = (14 - 8.75) / (6 - 3)
= 5.25 / 3
= 1.75
So, the rate of change between Friend 3 and Friend 4 is 1.75.
d.) No, this table does not show a linear relationship.
e.) This table does not show a linear relationship because the rate of change is not constant. The rate of change between any two friends is 1.75, but the rates of change are not the same for all pairs.
f.) If the table of values represents a linear function, write the equation of the linear function: y = mx + b. Since the rates of change are not constant, the relationship is not linear, so an equation cannot be determined.
g.) Rate of change in the equation: Since the relationship is not linear, there is no single rate of change.
h.) N/A (Since the relationship is not linear, there is no rate of change to explain in this context.)
1.) Initial value in the equation: N/A (Since the relationship is not linear, there is no initial value to assign.)
j.) N/A (Since the relationship is not linear, there is no initial value to explain in this context.)