Question

suppose that y varies directly with x, and y = 12 when x = 15.
(a) write a direct variation equation that relates x and y.
equation:
(b) find y when x = 2.
y =

Explanation:

Part (a)

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 that \( y = 12 \) when \( x = 15 \). Substitute these values into the formula:
\( 12 = k \times 15 \)
To solve for \( k \), divide both sides by 15:
\( k=\frac{12}{15}=\frac{4}{5} \)

Step3: Write the direct variation equation

Substitute \( k = \frac{4}{5} \) back into \( y = kx \):
\( y=\frac{4}{5}x \)

Step1: Use the direct variation equation

We have the equation \( y=\frac{4}{5}x \) from part (a).

Step2: Substitute \( x = 2 \) into the equation

Substitute \( x = 2 \) into \( y=\frac{4}{5}x \):
\( y=\frac{4}{5}\times2 \)

Step3: Calculate the value of \( y \)

\( y=\frac{8}{5}=1.6 \)

Answer:

\( y = \frac{4}{5}x \)

Part (b)