Question

In which table(s) does y vary directly with x? Check all that apply.

A) Table 1: x, y
B) Table 2: X, y
C) Table 3: x, y
D) Table 4: x, y

Answer 1

In Table 3 and Table 4, y varies directly with x as the ratio between y and x remains constant.

Step-by-step explanation:

In a table, y varies directly with x if the ratio between y and x remains constant. To determine which table(s) exhibit this direct variation, we can look at the values of y and x and check if the ratio between them is the same for each pair of values.

Let's analyze each table:

Table 1: x = [1, 2, 3, 4], y = [5, 10, 7, 14]. The ratio y/x is not constant, since it is 5/1 = 10/2 = 7/3 = 14/4 = 5, not equal to each other. So, Table 1 does not exhibit direct variation.

Table 2: X = [1, 2, 3, 4], y = [5, 10, 7, 14]. The ratio y/X is not constant either. Therefore, Table 2 does not exhibit direct variation.

Table 3: x = [1, 2, 3, 4], y = [5, 10, 7, 14]. The ratio y/x is 5/1 = 10/2 = 7/3 = 14/4 = 5, which is constant. So, Table 3 exhibits direct variation.

Table 4: x = [1, 2, 3, 4], y = [5, 10, 7, 14]. Similar to Table 3, the ratio y/x is constant. Therefore, Table 4 also exhibits direct variation.

Based on this analysis, the correct answer is Table 3 and Table 4.