Question

suppose that y varies directly with x, and y = 3 when x = 15. (a) write a direct variation equation that relates x and y. equation: (b) find y when x = 10. y =

Explanation:

Step1: Recall direct variation formula

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

Step2: Find the constant \( k \)

We know \( y = 3 \) when \( x = 15 \). Substitute these values into the formula: \( 3 = k \times 15 \). Solve for \( k \) by dividing both sides by 15: \( k=\frac{3}{15}=\frac{1}{5} \).

Step3: Write the direct variation equation

Substitute \( k = \frac{1}{5} \) back into \( y = kx \). So the equation is \( y=\frac{1}{5}x \).

Step4: Find \( y \) when \( x = 10 \)

Use the equation \( y=\frac{1}{5}x \). Substitute \( x = 10 \): \( y=\frac{1}{5}\times10 = 2 \).

Answer:

(a) Equation: \( y=\frac{1}{5}x \)
(b) \( y = 2 \)