Question

Conversion of square feet to square yard can be represented by direct variation. 3 yd.² are equivalent to 27 ft.². What Y represent the number of square yards in Exton number of square feet. Then why varies directly with X. What is the constant variation?

Answer 1

The constant of variation for converting square feet to square yards in direct variation is 9, based on the fact that 1 square yard is equivalent to 9 square feet.

Step-by-step explanation:

The conversion of square feet to square yards is a common measurement challenge in mathematics that can be represented by direct variation. Because 1 yard is equivalent to 3 feet, we can square both sides to find that 1 square yard is equal to 9 square feet. Thus, if 3 square yards are equivalent to 27 square feet, we see a direct relationship where the constant of variation is the square of the conversion factor between feet and yards. The constant of variation, k, can be found by dividing the number of square feet by the number of square yards, leading to k = 27 ft² / 3 yd² = 9 ft²/yd². This means that for any given number of square feet, x, the corresponding number of square yards, y, can be found using the direct variation equation y = x/9.