Proportional relationship in tables

Answer 1

In a proportional relationship, the values in one column of a table are directly proportional to the values in another column. This means that multiplying the values in one column by a constant will give us the corresponding values in the other column.

For example, let's consider a table where the first column represents the number of hours worked and the second column represents the amount of money earned:

| Hours Worked | Money Earned |
|--------------|--------------|
| 1 | $10 |
| 2 | $20 |
| 3 | $30 |
| 4 | $40 |

In this table, we can see that the money earned is directly proportional to the number of hours worked. Each hour worked results in $10 earned. Thus, we can say that there is a proportional relationship between the hours worked and the money earned.

A proportional relationship can also be shown in a table where the values are not in a continuous sequence:

| Number of Apples | Cost (in dollars) |
|------------------|------------------|
| 2 | $1.00 |
| 5 | $2.50 |
| 10 | $5.00 |
| 15 | $7.50 |

In this example, the cost of apples is directly proportional to the number of apples. Each apple costs $0.50, which means that there is a proportional relationship between the number of apples and the cost.

Proportional relationships are usually represented by a linear equation in the form of y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality. The constant of proportionality represents the ratio between the two variables.

In the first example, the linear equation representing the relationship between the hours worked (x) and the money earned (y) is y = 10x. The constant of proportionality, in this case, is 10, which represents the $10 earned per hour.

In the second example, the linear equation representing the relationship between the number of apples (x) and the cost (y) is y = 0.50x. The constant of proportionality, in this case, is 0.50, which represents the $0.50 cost per apple.

Proportional relationships in tables are helpful in understanding the relationship between two variables and can be used to make predictions or solve problems involving these variables.