Question

Each table represents a proportional relationship. For each, find the constant of proportionality, and complete the equation that represents the relationship. Use decimal notation if necessary.

Answer 1

Explanation:

To find the constant of proportionality and complete the equation representing a proportional relationship, we need to examine the given tables and look for a pattern in the values.

Let's take an example of one of the tables to illustrate the process:

Table 1:

x | y

-----

1 | 4

2 | 8

3 | 12

To find the constant of proportionality, we need to determine the ratio between the values of y and x for each pair of corresponding values. The constant of proportionality is the same for all pairs.

Let's calculate the ratios for each pair in Table 1:

4/1 = 8/2 = 12/3 = 4

The ratio is consistent for all pairs, which means the constant of proportionality is 4.

To complete the equation representing the relationship, we can use the formula:

y = kx

where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.

Using the constant of proportionality we found (k = 4), the equation representing the relationship is:

y = 4x

This equation indicates that y is four times the value of x.