Question

suppose that y varies directly with x, and y = 8 when x = 20.
(a) write a direct variation equation that relates x and y.
equation:
(b) find y when x = 7.
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 \( y = 8 \) when \( x = 20 \). Substitute into \( y = kx \):
\( 8 = k \times 20 \)
Solve for \( k \): \( k=\frac{8}{20}=\frac{2}{5} \).

Step3: Write the variation equation

Substitute \( k = \frac{2}{5} \) into \( y = kx \):
\( y=\frac{2}{5}x \).

Step4: Find \( y \) when \( x = 7 \)

Substitute \( x = 7 \) into \( y=\frac{2}{5}x \):
\( y=\frac{2}{5}\times7=\frac{14}{5}=2.8 \).

Answer:

(a) Equation: \( y = \frac{2}{5}x \)
(b) \( y = \frac{14}{5} \) (or \( 2.8 \))