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. It can be expressed as y = kx, where k is a non-zero constant.

Front

If y varies directly with x, what does that imply about their relationship?

Back

It implies that as x increases or decreases, y will increase or decrease proportionally, maintaining a constant ratio.

Front

How do you find the constant of variation (k) in a direct variation problem?

Back

To find the constant of variation (k), you can use the formula k = y/x, where y and x are known values from the direct variation.

Front

Given y = 39 when x = 3, what is the constant of variation (k)?

Back

k = 39/3 = 13.

Front

If y = 15 when x = 12, what is the value of y when x = 32 in a direct variation?

Back

Using the constant of variation, k = 15/12 = 1.25. Then, y = kx = 1.25 * 32 = 40.

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 = 8 when x = 2, what is the value of x when y = 16?

Back

Since y varies directly with x, if y doubles (from 8 to 16), x will also double. Therefore, x = 4.

Front

What happens to y if x is halved in a direct variation?

Back

If x is halved, y will also be halved, maintaining the direct proportionality.

Front

How can you determine if a set of values represents a direct variation?

Back

You can determine if a set of values represents a direct variation by checking if the ratio y/x is constant for all pairs of values.

Front

What is the graphical representation of direct variation?

Back

The graphical representation of direct variation is a straight line that passes through the origin (0,0) in the coordinate plane.