Direct Variation Practice #1

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 variation.

Front

What is the constant of proportionality in direct variation?

Back

The constant of proportionality, denoted as k, is the constant factor that relates the two variables in a direct variation. It is the ratio of y to x.

Front

How can you determine if a graph represents direct variation?

Back

A graph represents direct variation if it is a straight line that passes through the origin (0,0).

Front

What is the equation of a direct variation if k = 5?

Back

The equation of the direct variation is y = 5x.

Front

If y varies directly with x and y = 12 when x = 3, what is the constant of variation k?

Back

k = 4, since y = kx implies 12 = k(3) => k = 12/3 = 4.

Front

If Trina earns $187.15 for 19 hours of work, how much does she earn per hour?

Back

She earns approximately $9.84 per hour, calculated as $187.15 / 19 hours.

Front

If the relationship between two variables is not linear, can it still be a direct variation?

Back

No, direct variation must be linear and pass through the origin.

Front

What is the formula to find the value of y in direct variation?

Back

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

Front

If k = 8, what is the value of y when x = 2?

Back

y = 16, since y = 8(2).

Front

What does it mean if there is no constant of proportionality in a relationship?

Back

It means that the relationship is not a direct variation; the ratio of y to x is not constant.