Direct Variation/ Constant of Proportionality

Front

What is Direct Variation?

Back

Direct Variation is a relationship between two variables where one variable is a constant multiple of the other. It can be expressed in the form y = kx, where k is the constant of proportionality.

Front

What is the Constant of Proportionality?

Back

The Constant of Proportionality (k) is the constant factor that relates two variables in a direct variation. It represents how much one variable changes in relation to another.

Front

Write the equation for a direct variation where y is 56.70 when x is 6.

Back

56.70 = 6x

Front

If y = 14x, what is the constant of proportionality?

Back

14

Front

How do you find the constant of proportionality from a direct variation equation?

Back

To find the constant of proportionality, rearrange the equation y = kx to solve for k: k = y/x.

Front

If a company sells 8 home theaters for $500 spent on advertising, what is the constant of proportionality?

Back

The constant of proportionality is 8/500 = 0.016.

Front

What does the graph of a direct variation look like?

Back

The graph of a direct variation is a straight line that passes through the origin (0,0).

Front

If y varies directly with x and y = 30 when x = 5, what is the constant of proportionality?

Back

k = y/x = 30/5 = 6.

Front

In the equation y = kx, what does 'k' represent?

Back

'k' represents the constant of proportionality in a direct variation.

Front

If a car travels 80 miles in 2 hours, what is the rate of travel in miles per hour?

Back

The rate of travel is 80 miles / 2 hours = 40 miles per hour.