Question

suppose that y varies directly with x, and y = 15 when x = 24.
(a) write a direct variation equation that relates x and y.
equation:
(b) find y when x = 3.
y =

Explanation:

Step1: Recall direct variation formula

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

Step2: Find the constant \( k \)

Given \( y = 15 \) when \( x = 24 \), substitute into \( y = kx \):
\( 15 = k \times 24 \), so \( k=\frac{15}{24}=\frac{5}{8} \).

Step3: Write the direct variation equation

Substitute \( k = \frac{5}{8} \) into \( y = kx \):
Equation: \( y=\frac{5}{8}x \)

Step4: Find \( y \) when \( x = 3 \)

Substitute \( x = 3 \) into \( y=\frac{5}{8}x \):
\( y=\frac{5}{8}\times3=\frac{15}{8}=1.875 \)

Answer:

s:
(a) Equation: \( y=\frac{5}{8}x \)
(b) \( y = \frac{15}{8} \) (or \( 1.875 \))