Exploring Direct and Inverse Variation Concepts

Coach Latham provides a comprehensive review of direct and inverse variation, focusing on their characteristics, graphing techniques, and problem-solving strategies. Direct variation is explained as a linear relationship passing through the origin, represented by y = kx, where k is the constant of variation. Graphing examples and problem-solving exercises are included to reinforce understanding. Inverse variation is introduced as a relationship where the product of two variables is constant, with examples and identification exercises. The video aims to prepare students for the SOL test by enhancing their understanding of these mathematical concepts.

What is a common characteristic of graphs representing direct variation?

• They do not intersect the x-axis.

• They are non-linear curves.

• They pass through the origin.

• They have a negative slope.

What does the constant 'k' represent in the equation y = kx?

• The x-intercept of the graph

• The curvature of the graph

• The y-intercept of the graph

• The slope of the line

If a worker earns $2 per hour, how much will they earn after 3 hours?

• $6

• $8

• $10

• $5

Which graph represents a direct variation?

• A graph that does not pass through the origin

• A graph with a slope of zero

• A graph that passes through the origin with a positive slope

• A graph with a vertical line

What is the value of y when x is 30 and k is 3 in the equation y = kx?

• 120

• 60

• 30

• 90

What is the equation form for inverse variation?

• y = k + x

• y = kx

• y = k/x

• x = k - y

In the context of inverse variation, if xy = 6, what is y when x = 2?

• 12

• 3

• 6

• 4

Which scenario is an example of inverse variation?

• Pressure and volume of a gas at constant temperature

• Distance traveled over time at constant speed

• Cost of goods based on quantity purchased

• Salary based on hours worked

What is the constant k in the inverse variation equation where p * v = 2000?

• 1500

• 2000

• 1000

• 500

If x * y = 10 in an inverse variation, what is y when x = 5?

• 1

• 10

• 5

• 2