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 graph of a direct variation?

Back

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

Front

What does the constant 'k' represent in the equation y = kx?

Back

The constant 'k' represents the constant of variation, indicating how much y changes for a unit change in x.

Front

If y varies directly with x, what is the value of y when x = 5 and k = 3?

Back

y = kx = 3 * 5 = 15.

Front

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

Back

(0, 0) - the origin.

Front

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

Back

k = y/x = 12/4 = 3.

Front

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

Back

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

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

If y varies directly with x and y = 39 when x = 3, what is y when x = 2?

Back

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

Front

If x and y vary directly, what is the missing value in the points (x, 4) and (-14, -8)?

Back

x = 7.