8.5E 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 does the constant 'k' represent in Direct Variation?

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, and y = 20 when x = 4, what is the value of k?

Back

k = y/x = 20/4 = 5.

Front

If y = 15 when x = 3, what is the equation of the direct variation?

Back

The equation is y = 5x, since k = 15/3 = 5.

Front

How do you determine if two quantities vary directly?

Back

Two quantities vary directly if their ratio remains constant.

Front

If y varies directly with x and y = 60 when x = 12, what is y when x = 20?

Back

y = kx; k = 60/12 = 5; y = 5 * 20 = 100.

Front

What is the graph of a direct variation relationship?

Back

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

Front

If the equation of a direct variation is y = 8x, what is the value of y when x = 5?

Back

y = 8 * 5 = 40.

Front

What happens to y if x is doubled in a direct variation?

Back

If x is doubled, y will also double, since they are directly proportional.

Front

In a direct variation, if k is negative, what does that imply about the relationship?

Back

If k is negative, it implies that as x increases, y decreases, indicating an inverse relationship.