Direct Variations Check

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, typically expressed in the form y = kx, where k is a non-zero constant.

Front

How can you identify a direct variation from an equation?

Back

An equation represents direct variation if it can be rearranged to the form y = kx, meaning there is no constant term added or subtracted.

Front

If y varies directly with x, what happens to y when x is doubled?

Back

If y varies directly with x, then doubling x will also double y.

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 relationship, represented as k = y/x.

Front

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

Back

A set of points represents direct variation if the ratio of y to x is constant for all points.

Front

What does a graph of a direct variation look like?

Back

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

Front

If a table of values shows (2, 4) and (3, 6), does it represent direct variation?

Back

Yes, because the ratio of y to x is constant (2 in this case).

Front

What is the formula to find the constant of variation from a direct variation problem?

Back

The formula is k = y/x, where y is the dependent variable and x is the independent variable.

Front

In the context of direct variation, what does it mean if k is negative?

Back

If k is negative, it indicates that as one variable increases, the other variable decreases, but the relationship is still linear.

Front

Can direct variation occur with more than two variables?

Back

Yes, direct variation can occur with multiple variables, such as z = kxy, where z varies directly with both x and y.