Direct Variation

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is the constant of variation.

Front

What type of relationship is a direct variation?

Back

Proportional.

Front

What does the constant of variation represent in a direct variation equation?

Back

The constant of variation represents the rate at which one variable changes in relation to another. It is the factor by which one variable is multiplied to obtain the other.

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx, where k is the constant of variation.

Front

What does 'k' stand for in the direct variation equation?

Back

'k' stands for the constant of proportionality.

Front

If y = 3x, what is the constant of variation?

Back

The constant of variation is 3.

Front

If the equation is y = 5x, what does this tell you about the relationship between y and x?

Back

This indicates that y varies directly with x, and for every unit increase in x, y increases by 5.

Front

Determine if the relationship between the two quantities is a direct variation: y = 2x + 3. Explain your reasoning.

Back

No, this is not a direct variation because it includes a constant term (3) that does not allow for a proportional relationship.

Front

What is an example of a direct variation in real life?

Back

An example of direct variation is the relationship between distance and time when traveling at a constant speed.

Front

If y = 4x, what is the value of y when x = 2?

Back

When x = 2, y = 4(2) = 8.