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 the constant of variation.

Front

What does the constant of variation (k) represent?

Back

The constant of variation (k) represents the ratio of y to x in a direct variation relationship. It indicates how much y changes for a unit change in x.

Front

If y varies directly with x and k = 3, what is the equation?

Back

y = 3x

Front

Is the relationship y = 2x + 5 a direct variation?

Back

No, because direct variation must pass through the origin (0,0) and cannot have a constant term.

Front

If y = 10 when x = 5, what is the constant of variation?

Back

k = 2 (since k = y/x = 10/5).

Front

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

Back

Check if the ratio y/x is constant for all pairs of values.

Front

What is the graphical representation of direct variation?

Back

A straight line that passes through the origin (0,0).

Front

If y = 4 when x = 8, what is y when x = 16?

Back

y = 8 (since k = 0.5, y = 0.5 * 16).

Front

A recipe requires 2 cups of flour for every 3 cups of sugar. What is the constant of variation?

Back

k = 2/3 (flour to sugar ratio).

Front

If a car travels 120 miles in 2 hours, what is the constant of variation for speed?

Back

k = 60 miles per hour (speed = distance/time).