Understanding Variations in Mathematics

What is the equation for direct variation between x and y if y = 3 when x = 2?

• y = 2x

• y = 1.5x

• y = 4x

• y = (3/2)x

If y varies inversely with x and y = 4 when x = 2, what is the value of y when x = 8?

• 1

• 2

• 0

• -1

Graph the joint variation of z with x and y if z = kxy and k = 2, for x = 1, 2, 3 and y = 1, 2, 3.

• (2,2,6)

• (3,3,12)

• (1,1,3)

• The values of z for the combinations are: (1,1,2), (1,2,4), (1,3,6), (2,1,4), (2,2,8), (2,3,12), (3,1,6), (3,2,12), (3,3,18).

Write the equation for direct variation if y = 5 when x = 10.

• y = 10x

• y = 5x + 5

• y = 2x

• y = 0.5x

If y varies inversely with the square of x, and y = 3 when x = 2, what is the equation for this variation?

• y = 6/x

• y = 3x^2

• y = 12/x^2

• y = 24/x^2

In a direct variation, if y = 12 when x = 4, what is the constant of variation?

• 3

• 2

• 4

• 6

Solve for y in the inverse variation equation if k = 20 and x = 5.

• 8

• 4

• 10

• 2

If z varies jointly with x and y, and z = 30 when x = 2 and y = 3, what is the equation for z?

• z = 15xy

• z = 10xy

• z = 5xy

• z = 6xy

Interpret the meaning of the constant of variation in a direct variation scenario.

• The constant of variation represents the maximum value of the variables.

• The constant of variation indicates the rate of change between two directly related variables.

• The constant of variation is the initial value of the variables.

• The constant of variation is the difference between the two variables.

If the time taken to complete a task varies inversely with the number of workers, and it takes 10 hours for 2 workers, how long will it take for 5 workers?

• 4 hours

• 12 hours

• 8 hours

• 6 hours