Question

Which table has a constant of proportionality less than 5?

a. X 1 3 7
Y 6 18 42

b. X 1 2 3
Y 5 10 15

c. X 3 6 10
Y 21 35 70

d. X 4 5 6
Y 10 12.5 15

Answer 1

Table d has a constant of proportionality less than 5, with a value of 2.5, as determined by the consistent ratio of Y to X in the table.

Step-by-step explanation:

To find which table has a constant of proportionality less than 5, you must calculate the ratio of Y to X for each table and see if it remains constant for all values. The constant of proportionality is the ratio that you get when you divide the second number (Y) by the first number (X).

• For Table a, this ratio is 6/1 = 6, 18/3 = 6, and 42/7 = 6, which means the constant is 6.
• For Table b, the constant of proportionality is 5/1 = 5, 10/2 = 5, and 15/3 = 5, which means the constant is 5.
• For Table c, the ratios are 21/3 = 7, 35/6 ≈ 5.83, and 70/10 = 7, so the constant here is also greater than 5.
• Lastly, for Table d, the constant of proportionality is 10/4 = 2.5, 12.5/5 = 2.5, and 15/6 = 2.5, showing that the constant is 2.5, which is less than 5.

Therefore, the table with a constant of proportionality less than 5 is Table d.