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 constant of variation in direct variation?

Back

The constant of variation (k) is the ratio of y to x in a direct variation, represented as k = y/x.

Front

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

Back

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

Front

If y varies directly with x and k = 13, what is the equation of the variation?

Back

y = 13x.

Front

What ordered pair does a direct variation always go through when graphed?

Back

(0, 0).

Front

If y = 14 when x = 6, what is the constant of variation?

Back

k = y/x = 14/6 = 7/3.

Front

What is the equation representing the direct variation if y = 14 when x = 6?

Back

y = (7/3)x.

Front

Is the relationship y = 5x a direct variation?

Back

Yes, because it can be expressed in the form y = kx.

Front

If y = 26 when x = 2, what is the value of y when x = 3 in a direct variation?

Back

y = (26/2) * 3 = 39.

Front

How do you determine if a relationship is a direct variation?

Back

A relationship is a direct variation if it can be expressed as y = kx and passes through the origin (0, 0).