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 the constant of proportionality.

Front

If y varies directly with x, what does that mean?

Back

It means that as x increases or decreases, y changes in a proportional manner. The ratio y/x remains constant.

Front

What is the constant of proportionality in direct variation?

Back

The constant of proportionality (k) is the constant factor that relates the two variables in a direct variation equation, expressed as y = kx.

Front

If y = 39 when x = 3, what is the constant of proportionality?

Back

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

Front

If y = 2 when x = 6, what is the value of y when x = 12?

Back

y = kx; k = 2/6 = 1/3; y = (1/3) * 12 = 4.

Front

If y = 20 when x = 5, what is the value of y when x = 10?

Back

k = 20/5 = 4; y = 4 * 10 = 40.

Front

How do you find y when x is given in a direct variation problem?

Back

Use the formula y = kx, where k is the constant of proportionality.

Front

If y = 132 when x = 11, what is y when x = 17?

Back

k = 132/11 = 12; y = 12 * 17 = 204.

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx.

Front

If y = 15 when x = 195, what is the value of x when y = 9?

Back

k = 15/195 = 1/13; x = 9/(1/13) = 117.