Question

suppose that y varies directly with x, and y = 21 when x = 3. (a) write a direct variation equation that relates x and y. equation: (b) find y when x = -2. y =

Explanation:

Step1: Recall direct variation formula

Direct variation is \( y = kx \), where \( k \) is the constant of variation.

Step2: Find \( k \) using given values

We know \( y = 21 \) when \( x = 3 \). Substitute into \( y = kx \):
\( 21 = k \times 3 \). Solve for \( k \): \( k=\frac{21}{3}=7 \).
So the direct variation equation is \( y = 7x \).

Step3: Find \( y \) when \( x = -2 \)

Use the equation \( y = 7x \). Substitute \( x = -2 \):
\( y = 7\times(-2)= -14 \).

Answer:

(a) Equation: \( y = 7x \)
(b) \( y = -14 \)