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. It can be expressed as y = kx, where k is the constant of proportionality.

Front

What does the equation y = kx represent?

Back

The equation y = kx represents a direct variation, where y varies directly with x, and k is the constant of proportionality.

Front

How do you find the unit rate from a total cost?

Back

To find the unit rate, divide the total cost by the number of units. For example, if $3.60 is for 3 pounds of apples, the unit rate is $3.60 / 3 = $1.20 per pound.

Front

If y varies directly with x, and y = 84 when x = 16, what is the constant of proportionality (k)?

Back

k = y/x = 84/16 = 5.25.

Front

If Hayden reads 12 pages in 4 minutes, how many pages can he read in 17 minutes?

Back

Using direct variation, if he reads 3 pages per minute (12 pages / 4 minutes), then in 17 minutes he can read 3 * 17 = 51 pages.

Front

What is the constant of proportionality if y = 15 when x = 195?

Back

k = y/x = 15/195 = 1/13.

Front

If y varies directly with x, and k = 3, what is y when x = 10?

Back

y = kx = 3 * 10 = 30.

Front

What is the relationship between the variables in a direct variation?

Back

In a direct variation, as one variable increases, the other variable also increases, and vice versa.

Front

If y = 2 when x = 4, what is the value of k?

Back

k = y/x = 2/4 = 0.5.

Front

How can you determine if a relationship is a direct variation?

Back

A relationship is a direct variation if the ratio of y to x is constant for all pairs of values.