Question

If y varies directly as x, find the constant of variation and the direct variation equation for the situation

y=18 when x=10

Answer 1

Constant of variation = 1.8

Direct variation equation for the situation: y = 1.8x

Explanation:

The general direct variation equation is given by:

y = kh, where

• "y varies directly as x",
• and k is the constant of proportionality (aka variation).

Finding the constant of variation:

Since we're told that y = 18 when x = 10, we can find k (the constant of variation) by substituting 18 for y and 10 for x in the direct variation equation:

(18 = 10k) / 10

1.8 = k

Thus, the constant of variation (k) is 1.8.

Finding the direct variation equation for the situation:

Therefore, y = 1.8x is the direct variation equation for the situation.