Answer:
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.