Question

suppose that y varies directly with x, and y = 4 when x = 20.
(a) write a direct variation equation that relates x and y.
equation:
(b) find y when x = 9.
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 \( y = 4 \) when \( x = 20 \). Substitute these values into the formula: \( 4 = k \times 20 \). Solve for \( k \) by dividing both sides by 20: \( k=\frac{4}{20}=\frac{1}{5} \).

Step3: Write the direct variation equation

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

Step4: Find \( y \) when \( x = 9 \)

Use the equation \( y=\frac{1}{5}x \). Substitute \( x = 9 \): \( y=\frac{1}{5}\times9=\frac{9}{5}=1.8 \).

Answer:

(a) Equation: \( y = \frac{1}{5}x \)
(b) \( y = \frac{9}{5} \) (or \( 1.8 \))