Direct Variation

Front

What is the Direct Variation Equation?

Back

Y = kx, where k is the constant of variation.

Front

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

Back

It implies that as x increases or decreases, y increases or decreases proportionally.

Front

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

Back

The constant of variation (k) is the ratio of y to x in the equation y = kx.

Front

How do you find the constant of variation if y = 12 when x = 15?

Back

k = y/x = 12/15 = 0.8.

Front

If y = 16, what is the value of x when y varies directly with x and k = 0.8?

Back

x = y/k = 16/0.8 = 20.

Front

What does it mean if y = 5x in the context of distance and time?

Back

It means that for every mile (x), it takes 5 seconds (y) to hear the thunder after seeing the lightning.

Front

In a direct variation, if y = 39 when x = 3, how do you find y when x = 2?

Back

First, find k: k = y/x = 39/3 = 13. Then, y = kx = 13*2 = 26.

Front

Which of the following equations represents a direct variation: y = -2x or y = x + 3?

Back

y = -2x represents a direct variation because it can be expressed in the form y = kx.

Front

What is the graphical representation of a direct variation?

Back

A straight line that passes through the origin (0,0).

Front

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

Back

Check if the ratio of y to x is constant for all points.