Question

Suppose y varies directly with x, and y = 14 when x = 2. What direct variation equation relates x and y? What is the value of y when x = 6? Explain. Show your work

A. The equation y = 2x relates x and y. When x = 6, y =2(6) or 12.
B. The equation y = 14x relates x and y. When x = 6, y =14(6) or 84.
C. The equation y = 7x relates x and y. When x = 6, y =7(6) or 42.

Answer 1

Answer: C. The equation y = 7x relates x and y. When x = 6, y =7(6) or 42.

Explanation:

Using direct variation with the formula:

y = kx

Since y =14, when x = 2.

y = kx

14 = 2k

k = 14/2

k = 7

Therefore, y = 7x

The value of y when x = 6 will be:

y = kx

y = 6k

Recall that k = 7

y = 6 × 7

y = 42

Therefore, the equation y = 7x relates x and y. When x = 6, y =7(6) or 42.