Question

1. the variables x and y vary inversely, and y = -4 when x = 5. use the given values to write an equation relating x and y. then find y when x = 3. the inverse variation equation is a \square. when x = 3, b y = \square.

Explanation:

Step1: Recall inverse variation formula

The formula for inverse variation is \( y=\frac{k}{x} \) (or \( xy = k \)), where \( k \) is the constant of variation.

Step2: Find the constant \( k \)

We know that \( y=-4 \) when \( x = 5 \). Substitute these values into \( xy=k \):
\( 5\times(-4)=k \)
\( k=-20 \)

Step3: Write the inverse variation equation

Substitute \( k = - 20 \) into \( y=\frac{k}{x} \), we get \( y=\frac{-20}{x} \) (or \( xy=-20 \)).

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

Substitute \( x = 3 \) into \( y=\frac{-20}{x} \):
\( y=\frac{-20}{3} \)

Answer:

a. \( y = \frac{-20}{x} \) (or \( xy=-20 \))
b. \( y=-\frac{20}{3} \)