Exploring Direct Variation in Algebra

This video tutorial explains the concept of direct variation, a linear relationship between two variables where one variable is a constant multiple of the other. It covers how to identify direct variation, calculate the constant of variation (K), and solve problems using the direct variation equation y = KX. The tutorial includes examples and applications, such as determining if data in tables represent direct variation and solving real-world problems like calculating walking distances over time.

What is the relationship between X and Y in direct variation?

• X and Y are inversely proportional.

• X and Y have no relationship.

• Y varies directly with X.

• Y is always greater than X.

If Y varies directly with X and Y = 8 when X = 2, what is the constant of variation (K)?

• 2

• 6

• 4

• 8

Given the equation Y = 4X, what is the value of Y when X = 7?

• 11

• 21

• 35

• 28

If Y = 9 when X = -4, what is the constant of variation (K)?

• -2.25

• -4.5

• -1.5

• -2.75

For the table with values (X, Y): (2, 4), (5, 10), (7, 14), what is the constant of variation (K)?

• 2

• 3

• 1

• 4

Does Y vary directly with X in the table with values (X, Y): (1, 3), (3, 5), (7, 12)?

• Yes, because K is constant.

• No, because K is not constant.

• Yes, because Y is always greater than X.

• No, because X is always greater than Y.

For the table with values (X, Y): (4, 12), (7, 21), (-9, -27), what is the constant of variation (K)?

• 5

• 3

• 2

• 4

If Karen can walk 2 miles in 25 minutes, what is the constant of variation (K) in miles per minute?

• 0.1

• 0.06

• 0.08

• 0.04

How many miles can Karen walk in one hour if she walks 2 miles in 25 minutes?

• 4.2 miles

• 4.5 miles

• 4.8 miles

• 5 miles

What is the equation for the distance Karen walks (Y) in terms of time (X) in minutes?

• Y = 2/25 * X

• Y = 25X

• Y = 2X

• Y = 25/2 * X