Proportional Relationships
If the variables x and y are in a proportional relationship, then:
y = kx
Where k is the constant of proportionality that can be found as follows:
[tex]k=\frac{y}{x}[/tex]
If we are given a pair of values (x, y), we can find the value of k and use it to fill the rest of the table.
For example, Table 1 relates the cost y of x pounds of some items. We are given the pair (2, 2.50). We can calculate the value of k:
[tex]k=\frac{2.50}{2}=1.25[/tex]
Now, for each value of x, multiply by this factor and get the value of y. For example, for x = 3:
y = 1.25 * 3 = 3.75
This value is also given and verifies the correct proportion obtained above.
For x = 4:
y = 1.25 * 4 = 5
For x = 7:
y = 1.25 * 7 = 8.75
For x = 10:
y = 1.25 * 10 = 12.50
Now for table 2, we are given the pair (3, 4.5) which gives us the value of k:
[tex]k=\frac{4.5}{3}=1.5[/tex]
Apply this constant for the rest of the table.
For x = 4:
y = 1.5 * 4 = 6
For x = 5:
y = 1.5 * 5 = 7.50
For x = 8:
y = 1.5 * 8 = 12
The last column doesn't give us the value of x but the value of y, so we need to solve for x:
[tex]y=k\cdot x\text{ }=>\text{ }x=\frac{y}{k}[/tex]
For y = 15:
[tex]x=\frac{15}{1.5}=10[/tex]
