Direct Variation/Constant of Variation and a few functions

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

Front

What is the Constant of Variation?

Back

The Constant of Variation (k) is the constant ratio of the dependent variable to the independent variable in a direct variation relationship.

Front

How can you identify if a table represents a function?

Back

A table represents a function if each input (x-value) is associated with exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

Front

What does the equation y = 0.10x + 45 represent?

Back

This equation represents a linear relationship where the cost y of a cell phone plan increases by $0.10 for each text message x sent or received, plus a base fee of $45.

Front

Write the equation for the cost of x reams of paper if 2 reams cost $5.10.

Back

The equation is y = 2.55x, where y is the total cost and x is the number of reams.

Front

What is the significance of the slope in a direct variation equation?

Back

The slope represents the constant of variation, indicating how much the dependent variable changes for each unit change in the independent variable.

Front

Can a set of ordered pairs represent a function?

Back

Yes, a set of ordered pairs can represent a function if no x-value is repeated with different y-values.

Front

What does it mean if there is no constant of variation in an equation?

Back

It means that the dependent variable does not change in a consistent ratio with the independent variable, indicating no direct variation.

Front

If y = 9.50x, what does the constant of variation represent?

Back

The constant of variation is 9.50, meaning that each movie ticket costs $9.50.

Front

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

Back

A relationship is a direct variation if it can be expressed in the form y = kx, where k is a non-zero constant.