Inverse Variation Equations Identify

Apply inverse variation to a real-life scenario: If the number of workers is inversely proportional to the time taken to complete a task, and 8 workers can complete the task in 6 hours, how long will it take for 12 workers to complete the same task?

• 10 hours

• 4 hours

• 5 hours

• 2 hours

Answer explanation

Using inverse variation, we have 8 workers completing the task in 6 hours. The product of workers and time is constant: 8 * 6 = 48. For 12 workers, time = 48 / 12 = 4 hours. Thus, it will take 12 workers 4 hours to complete the task.

Apply inverse variation to a real-life scenario: If the speed of a car is inversely proportional to the time taken to reach the destination, and a car traveling at 60 mph reaches the destination in 4 hours, how long will it take for a car traveling at 80 mph to reach the same destination?

• 2 hours

• 3 hours

• 4 hours

• 5 hours

Answer explanation

Since speed and time are inversely proportional, we can use the relationship: speed1 × time1 = speed2 × time2. Here, 60 mph × 4 hours = 80 mph × time2. Solving gives time2 = 3 hours.

y varies inversely with x, and y is 0.5 when x is 4. Which equation represents this situation?

• y= 2x

• y= 2/x

• y= 4x

• y= x/2

Answer explanation

Since y varies inversely with x, we can express this as y = k/x, where k is a constant. Given y = 0.5 when x = 4, we find k = 2. Thus, the equation is y = 2/x, which is the correct choice.

Does the equation show an inverse variation? 
y=10/x

• yes

• no

Which of the following are true for INVERSE variation? Select all that apply.

• y = kx

• y = k / _x

• k = ^y / _x

• k = xy

• y = x / k

Tell whether x and y show an inverse variation, linear relationship, or neither.

• linear relationship

• inverse variation

• neither

What is the constant (k) in this inverse variation?

• 12

• 24

• 48

• Not enough information given

Determine the type of variation:

• Linear

• Inverse

What kind of variation is shown in the graph?

• Direct

• Inverse

Does the table show an inverse variation?

• Yes

• No