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

What is the equation of a direct variation?

Back

The equation of a direct variation is y = kx, where k is the constant of variation.

Front

If y varies directly with x and k = 5, what is the equation?

Back

y = 5x

Front

How can you identify a direct variation from a graph?

Back

A graph represents direct variation if it is a straight line that passes through the origin (0,0).

Front

What does it mean if y = 0 when x = 0 in direct variation?

Back

It means that the relationship is consistent with direct variation, as both variables are zero.

Front

If y = 12 when x = 4, what is the constant of variation (k)?

Back

k = 3 (since y = kx, 12 = k(4) => k = 12/4 = 3).

Front

In a direct variation, if y = 20 when x = 5, what is y when x = 10?

Back

y = 40 (since k = 4, y = kx => y = 4(10) = 40).

Front

Is the relationship y = 2x + 3 a direct variation?

Back

No, because it does not pass through the origin.

Front

What is the constant of variation if y = 15 when x = 3?

Back

k = 5 (since y = kx, 15 = k(3) => k = 15/3 = 5).

Front

If y varies directly with x and y = 30 when x = 6, what is y when x = 2?

Back

y = 10 (k = 5, so y = kx => y = 5(2) = 10).