A.2D Synthesis - 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

In Direct Variation, '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 = 10 when x = 2, what is the value of k?

Back

k = y/x = 10/2 = 5.

Front

Write the equation of direct variation for the relationship where y = 15 when x = 3.

Back

y = 5x.

Front

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

Back

A relationship is a direct variation if the ratio y/x is constant for all pairs of (x, y) values.

Front

What is the graph of a direct variation equation like?

Back

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

Front

If y varies directly with x and y = 20 when x = 4, what is y when x = 10?

Back

Using k = 5, y = 5 * 10 = 50.

Front

What is the relationship between direct variation and proportionality?

Back

Direct variation indicates a proportional relationship where the ratio of y to x remains constant.

Front

If the equation of direct variation is y = 3x, what is the value of y when x = 7?

Back

y = 3 * 7 = 21.

Front

Can direct variation have a negative constant?

Back

Yes, direct variation can have a negative constant, indicating that as one variable increases, the other decreases.