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, typically expressed as y = kx, where k is a non-zero constant.

Front

How do you find the unit rate from a given cost and quantity?

Back

To find the unit rate, divide the total cost by the quantity. For example, if the cost is $3.60 for 3 pounds, the unit rate is $3.60 ÷ 3 = $1.20 per pound.

Front

What is the constant of variation in a direct variation equation?

Back

The constant of variation (k) is the non-zero constant that relates the two variables in a direct variation equation, represented as y = kx.

Front

How can you determine if a table represents a direct variation?

Back

A table represents direct variation if the ratio of y to x is constant for all pairs of values.

Front

What characteristics define a graph of direct variation?

Back

A graph of direct variation is a straight line that passes through the origin (0,0) and has a constant slope.

Front

What does it mean if a graph does not show direct variation?

Back

If a graph does not show direct variation, it may not pass through the origin or may not have a constant slope, indicating a non-linear relationship.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if it is a straight line that passes through the origin.

Front

What is the difference between direct variation and inverse variation?

Back

Direct variation means that as one variable increases, the other variable also increases, while inverse variation means that as one variable increases, the other decreases.

Front

What is the formula for direct variation?

Back

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

Front

How do you solve for the constant of variation given a pair of values?

Back

To solve for the constant of variation (k), use the formula k = y/x, where y and x are the values from the direct variation.