the quantities in the data table are in a proportional relationship. Using the data in the table, show your work and explain how you know the table represents a proportional relationship
hours: 1,2,3,4 money: 9,18,27,36
To determine if the table represents a proportional relationship, we need to check if the ratio of money to hours is constant.
Ratio of Money to Hours:
For the first pair of values (1 hour and 9 money), the ratio is 9 / 1 = 9.
For the second pair of values (2 hours and 18 money), the ratio is 18 / 2 = 9.
For the third pair of values (3 hours and 27 money), the ratio is 27 / 3 = 9.
For the fourth pair of values (4 hours and 36 money), the ratio is 36 / 4 = 9.
Since the ratio of money to hours is constant at 9, we can conclude that the table represents a proportional relationship.
Alternatively, we can also verify this by determining if the values satisfy the equation y = kx, where y represents money, x represents hours, and k represents a constant. Let's check:
For the first pair of values (1 hour and 9 money):
9 = k * 1
k = 9
For the second pair of values (2 hours and 18 money):
18 = 9 * 2 (satisfies the equation)
For the third pair of values (3 hours and 27 money):
27 = 9 * 3 (satisfies the equation)
For the fourth pair of values (4 hours and 36 money):
36 = 9 * 4 (satisfies the equation)
Since all the values satisfy the equation y = kx, we can also confirm that the table represents a proportional relationship.