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.

Front

What is the formula for Direct Variation?

Back

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

Front

If $70 is earned in 5 hours, how much is earned in 1 hour?

Back

$14 per hour.

Front

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

Back

k = y/x = 39/3 = 13.

Front

If y = 8 when x = -4, what is the value of k?

Back

k = y/x = 8/(-4) = -2.

Front

If y varies directly with x and k = 5, what is y when x = 10?

Back

y = kx = 5 * 10 = 50.

Front

Is the equation y = 2x a direct variation?

Back

Yes, it is a direct variation because it can be expressed in the form y = kx.

Front

What does the graph of a direct variation look like?

Back

The graph is a straight line that passes through the origin (0,0).

Front

If y = 26 when x = 2, what is y when x = 4?

Back

y = 52, since y varies directly with x.