Direct Variation Flashcard

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 a non-zero constant.

Front

What does 'k' represent in the equation y = kx?

Back

In the equation y = kx, 'k' represents the constant of proportionality, which indicates how much y changes for a unit change in x.

Front

How can you identify a direct variation from a graph?

Back

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

Front

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

Back

To find the hourly wage, divide her earnings by the hours worked: $187.15 / 19 hours = $9.85 per hour.

Front

If a job pays $70 for 5 hours of work, what is the pay rate per hour?

Back

The pay rate is $70 / 5 hours = $14 per hour.

Front

What is the equation for direct variation if y varies directly as x and k = 8?

Back

The equation is y = 8x.

Front

If y = 3x, what is the value of y when x = 4?

Back

Substituting x = 4 into the equation gives y = 3(4) = 12.

Front

If the relationship between two variables is y = 5x, what happens to y if x is doubled?

Back

If x is doubled, y will also double. For example, if x = 2, then y = 5(2) = 10; if x = 4, then y = 5(4) = 20.

Front

What is the constant of proportionality in the equation y = 10x?

Back

The constant of proportionality is 10.

Front

If a car travels 60 miles in 1 hour, how far will it travel in 3 hours?

Back

In 3 hours, the car will travel 60 miles/hour * 3 hours = 180 miles.