Exploring Direct and Inverse Variation Concepts

This video tutorial covers the concepts of direct and inverse variation. It explains direct variation as a relationship where one variable is directly proportional to another, represented by the equation y = kx. Examples and real-world applications, such as Hook's Law, are provided to illustrate the concept. The video then introduces inverse variation, where one variable is inversely proportional to another, represented by y = k/x. Examples and applications, like the time required to empty a tank, are discussed. The tutorial concludes with a summary of key points.

What does it mean when we say 'Y varies directly as X'?

• Y decreases as X increases

• Y increases as X decreases

• Y increases as X increases

• Y is constant when X changes

What is the role of the constant K in the equation Y = KX?

• It is the exponent to which X is raised.

• It indicates the curvature of the graph.

• It determines the Y-intercept of the graph.

• It represents the slope of the line.

What is the graphical representation of direct variation?

• A hyperbola

• A straight line passing through the origin

• A horizontal line

• A parabola through the origin

How do you find the constant of proportionality when given Y = 28 and X = 7?

• Divide 28 by 7

• Multiply 28 by 7

• Add 28 to 7

• Subtract 7 from 28

According to Hooke's Law, if the mass is increased, what happens to the displacement?

• It decreases.

• It becomes zero.

• It remains constant.

• It increases.

What is the inverse variation equation if Y = 27 when X = 1/3?

• Y = 3X

• Y = X / 9

• Y = 9 / X

• Y = 9X

In inverse variation, if X increases, what happens to Y?

• Y increases.

• Y decreases.

• Y remains constant.

• Y becomes zero.

What does the constant K represent in the equation T = K / R?

• The total volume of the tank

• The efficiency of the pump

• The initial time required at a given rate

• The rate of flow per minute

How long will it take to empty a tank at a rate of 500 gallons per minute, if the constant K is 13,500?

• 60 minutes

• 45 minutes

• 27 minutes

• 30 minutes

If the rate of pumping is increased from 300 to 500 gallons per minute, what is the effect on the time required to empty the tank?

• It doubles.

• It decreases.

• It remains the same.

• It increases.