Direct Variation

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is the constant of proportionality.

Front

How do you find the constant of proportionality in a direct variation problem?

Back

To find the constant of proportionality (k), divide the value of y by the value of x (k = y/x).

Front

If y varies directly with x and y = 20 when x = 5, what is the constant of proportionality?

Back

The constant of proportionality is 4, calculated as k = 20/5.

Front

In a direct variation, if y = 132 when x = 11, what is the value of y when x = 17?

Back

The value of y when x = 17 is 204, calculated using the constant of proportionality.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of proportionality.

Front

What does it mean if two quantities do not vary directly?

Back

If two quantities do not vary directly, it means that the relationship between them cannot be expressed as y = kx for a constant k.

Front

How can you determine if a set of data represents direct variation?

Back

To determine if a set of data represents direct variation, check if the ratio of y to x is constant for all pairs of values.

Front

If Jim runs 6 miles in 46.8 minutes, how long will it take him to run 13.1 miles?

Back

It will take him approximately 102.18 minutes to run 13.1 miles, calculated using the ratio of miles to time.

Front

What is the relationship between direct variation and proportionality?

Back

Direct variation implies proportionality, meaning that as one variable increases, the other variable increases at a constant rate.

Front

Can a linear equation represent direct variation?

Back

Yes, a linear equation can represent direct variation if it passes through the origin (0,0).