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 non-zero constant that relates the two variables in a direct variation equation.

Front

If y varies directly with x, what does the graph look like?

Back

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

Front

What ordered pair does a direct variation always pass through?

Back

(0, 0) - This is the origin, where both x and y are zero.

Front

If y = 5 when x = 2, what is the constant of variation?

Back

k = y/x = 5/2 = 2.5.

Front

If y = 10 when x = 4, find y when x = 8 in direct variation.

Back

y = kx; k = 10/4 = 2.5; y = 2.5 * 8 = 20.

Front

Which equation represents direct variation?

Back

y = kx, where k is a constant.

Front

If y = 3 when x = 1, what is y when x = 5?

Back

y = 3 * 5 = 15.

Front

What is the relationship between x and y in direct variation?

Back

As x increases, y increases proportionally, and as x decreases, y decreases proportionally.

Front

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

Back

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