Understanding Direct and Inverse Variation

This video tutorial covers the concepts of direct and inverse variation. It explains how direct variation is represented by the equation Y = KX, where Y varies directly as X, and the constant K is the proportionality constant. Examples are provided to illustrate how to determine the direct variation equation and solve for unknowns. The video also discusses Hook's Law as a real-world application of direct variation. Inverse variation is introduced with the equation Y = K/X, where Y varies inversely as X. Examples demonstrate how to find the inverse variation equation and solve related problems. A real-world application involving the time to empty a tank is also explored.

What is the equation that represents a direct variation between two variables?

• Y = K - X

• Y = KX

• Y = K/X

• Y = K + X

In a direct variation, if Y = 28 when X = 7, what is the constant of proportionality?

• 2

• 5

• 3

• 4

Using the direct variation equation Y = 4X, what is Y when X = 3.5?

• 14

• 15

• 12

• 13

According to Hook's Law, if a spring stretches 12 cm with a 4 kg mass, what is the constant of proportionality?

• 4

• 5

• 3

• 2

In Hook's Law, if the constant of proportionality is 3, what is the displacement when the mass is 5 kg?

• 10 cm

• 12 cm

• 18 cm

• 15 cm

What is the equation that represents an inverse variation between two variables?

• Y = KX

• Y = K + X

• Y = K - X

• Y = K/X

In an inverse variation, if Y = 27 when X = 1/3, what is the constant of proportionality?

• 9

• 8

• 7

• 6

Using the inverse variation equation Y = 9/X, what is Y when X = 18?

• 1/2

• 1

• 3

• 2

If a pump empties a tank in 45 minutes at 300 gallons per minute, what is the constant of proportionality?

• 16,500

• 12,000

• 13,500

• 15,000

Using the inverse variation equation T = 13,500/R, how long will it take to empty the tank at 500 gallons per minute?

• 28 minutes

• 26 minutes

• 27 minutes

• 25 minutes