Students are selling t-shirt’s for a school fundraiser. The table shows the amount they raised.
Shirts Sold: 1, 2, 3, 4
Amount Raised: 4, 8, 12, 16
Complete each statement
The amount raised is the (Dependent or Independent) variable and the number of shirts sold is the (Dependent or Independent) variable.
The amount raised is the dependent variable and the number of shirts sold is the independent variable.
What is the constant of proportionality?
The constant of proportionality can be found by taking the ratio of the amount raised to the number of shirts sold.
For example, for the first data point (1 shirt sold, $4 raised), the ratio is 4/1 = 4.
Similarly, for each data point, the ratio is:
Second data point (2 shirts sold, $8 raised): 8/2 = 4
Third data point (3 shirts sold, $12 raised): 12/3 = 4
Fourth data point (4 shirts sold, $16 raised): 16/4 = 4
The constant of proportionality in this case is 4. This means that for every shirt sold, the amount raised is multiplied by 4.
Complete the equation to show the relationship between the number of shirts sold, x and the amount raised, y.
Y= ___X
Y = 4X
To determine which variable is the dependent variable and which one is the independent variable, we need to understand the relationship between the two variables.
In this case, the number of shirts sold is the independent variable because it is the variable that can be controlled or manipulated by the students. They can choose how many shirts they want to sell.
On the other hand, the amount raised is the dependent variable because it depends on the number of shirts sold. As more shirts are sold, the amount raised increases. The amount raised is influenced by the number of shirts sold.
So, to complete the statements:
1. The amount raised is the dependent variable.
2. The number of shirts sold is the independent variable.