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 the constant of variation.

Front

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

Back

The constant of variation (k) represents the ratio of y to x in a direct variation relationship, indicating how much y changes for a unit change in x.

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified from a graph if the line passes through the origin (0,0) and is straight, indicating a constant ratio between x and y.

Front

If y varies directly with x and y = 12 when x = 15, how do you find the constant of variation (k)?

Back

To find k, use the formula k = y/x. Here, k = 12/15 = 0.8.

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

If y = 5.25x, what is the constant of variation (k)?

Back

The constant of variation (k) is 5.25.

Front

How do you solve for x when given y in a direct variation equation?

Back

To solve for x, rearrange the equation y = kx to x = y/k.

Front

What is the relationship between x and y in a direct variation?

Back

In direct variation, as x increases, y increases proportionally, and as x decreases, y decreases proportionally.

Front

If a dishwasher uses 65 gallons of water to wash 5 loads of dishes, how do you find the constant of variation?

Back

To find the constant of variation, divide the total gallons of water by the number of loads: k = 65/5 = 13.

Front

What does it mean if two quantities vary directly?

Back

If two quantities vary directly, it means that they increase or decrease together at a constant rate.