Question

Need some help with table 2.Fill up tables of proportional relationships with missing Values.

Answer 1

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:

`k=(y)/(x)`

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:

`k=(2.50)/(2)=1.25`

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:

`k=(4.5)/(3)=1.5`

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:

`y=k\cdot x\text{ }=>\text{ }x=(y)/(k)`

For y = 15:

`x=(15)/(1.5)=10`