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 it mean if a table represents Direct Variation?

Back

A table represents Direct Variation if the ratio of the two variables remains constant for all pairs of values.

Front

How can you identify Direct Variation from a graph?

Back

A graph represents Direct Variation if it is a straight line that passes through the origin (0,0).

Front

What is the unit rate?

Back

The unit rate is the ratio of two measurements in which the second measurement is 1. It is often used to compare prices or speeds.

Front

If y varies directly with x, and y = 12 when x = 3, what is the constant of variation (k)?

Back

k = 4, because y = kx implies 12 = k(3), so k = 12/3 = 4.

Front

Does the equation y = 5x + 2 represent Direct Variation?

Back

No, because it does not pass through the origin; it has a y-intercept of 2.

Front

If the cost of 4 pounds of apples is $4.80, what is the cost per pound?

Back

$1.20 per pound.

Front

What is the formula for Direct Variation?

Back

The formula for Direct Variation is y = kx, where k is the constant of variation.

Front

If y = 10 when x = 2, what is the value of y when x = 5?

Back

y = 25, because k = 5 and y = kx.

Front

Does the following set of points (2, 4), (3, 6), (4, 8) represent Direct Variation?

Back

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