Question

got it? suppose y varies directly with x, and y = 10 when x = -2. what direct variation equation relates x and y? what is the value of y when x = -15?

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 that \( y = 10 \) when \( x = -2 \). Substitute these values into the formula:
\( 10 = k(-2) \)
To solve for \( k \), divide both sides by \( -2 \):
\( k = \frac{10}{-2} = -5 \)

Step3: Write the direct variation equation

Substitute \( k = -5 \) into \( y = kx \). The equation is \( y = -5x \).

Step4: Find \( y \) when \( x = -15 \)

Substitute \( x = -15 \) into the equation \( y = -5x \):
\( y = -5(-15) = 75 \)

Answer:

The direct variation equation is \( y = -5x \), and when \( x = -15 \), \( y = 75 \).