Question

write as a power function:
y varies directly with x
and y is 12 when x is 6.
? = x

Explanation:

Step1: Recall direct variation formula

For direct variation, the formula is \( y = kx \), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know that \( y = 12 \) when \( x = 6 \). Substitute these values into the formula \( 12 = k \times 6 \).
To solve for \( k \), divide both sides by 6: \( k=\frac{12}{6}=2 \).

Step3: Write the power function

Substitute \( k = 2 \) back into the direct variation formula \( y = kx \), we get \( y = 2x \).

Answer:

\( y = 2x \) (So the first box is \( y \) and the second box is \( 2 \))