Direct Variation, Rate of Change, 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 is the constant factor (k) that relates two proportional quantities in a direct variation. It represents the ratio of the two quantities.

Front

How do you find the Rate of Change?

Back

The Rate of Change is found by dividing the change in the dependent variable by the change in the independent variable, often expressed as (y2 - y1) / (x2 - x1).

Front

What does a negative Rate of Change indicate?

Back

A negative Rate of Change indicates that as one quantity increases, the other quantity decreases.

Front

What is the formula for calculating the Constant Rate of Change?

Back

The formula is: Constant Rate of Change = (Change in y) / (Change in x).

Front

If y varies directly with x, and k = 3, what is the equation?

Back

The equation is y = 3x.

Front

What does it mean if a graph represents a direct variation?

Back

If a graph represents a direct variation, it will be a straight line that passes through the origin (0,0).

Front

How can you identify the Constant of Proportionality from a table?

Back

You can identify the Constant of Proportionality by dividing the values of y by the corresponding values of x. If the ratio is constant, it is the constant of proportionality.

Front

What is the significance of the slope in a linear graph?

Back

The slope of a linear graph represents the Rate of Change between the two variables.

Front

If the temperature decreases from 88°F to 72°F over 4 hours, what is the Rate of Change?

Back

The Rate of Change is -4 degrees per hour.