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

Front

What is the Constant of Proportionality?

Back

The constant of proportionality (k) is the constant factor that relates two proportional quantities in a direct variation.

Front

If a car travels 120 miles in 2 hours, what is the constant of variation?

Back

k = 60 (miles per hour)

Front

What is the independent variable in a direct variation?

Back

The independent variable is the variable that is changed or controlled in an experiment, often represented on the x-axis.

Front

What is the dependent variable in a direct variation?

Back

The dependent variable is the variable that is measured or affected in an experiment, often represented on the y-axis.

Front

Does the equation y = 3x represent a direct variation?

Back

Yes, it represents a direct variation with a constant of proportionality k = 3.

Front

What ordered pair does a direct variation always go through when graphed?

Back

(0, 0) - This is the origin point.

Front

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

Back

k = 4.

Front

Is the relationship between x and y in the equation y = 2x + 1 a direct variation?

Back

No, because it does not pass through the origin (0, 0).

Front

What happens to y if x is doubled in a direct variation?

Back

y will also double, maintaining the constant ratio.