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 y = 7x + 3? Is this a direct variation?

Back

No, this is not a direct variation because it includes a constant term (3). Direct variation must pass through the origin (0,0).

Front

If 15 miles is represented by 3 centimeters on a map, how do you find the equivalent centimeters for 135 miles?

Back

Set up a proportion: 15 miles / 3 cm = 135 miles / x cm. Cross-multiply and solve for x to find that x = 27 cm.

Front

Write the equation for a situation where y is directly proportional to x, and y = 19.25 when x = 1.

Back

The equation is y = 19.25x.

Front

If Shawn earns $123.00 for 20 hours of work, how much will he earn for 31 hours?

Back

To find the pay for 31 hours, first find the rate: $123.00 / 20 hours = $6.15 per hour. Then, multiply by 31 hours: $6.15 * 31 = $190.65.

Front

In a direct variation, if y = 39 when x = 3, what is y when x = 2?

Back

To find y when x = 2, use the constant of variation k = y/x. Here, k = 39/3 = 13. Then, y = 13 * 2 = 26.

Front

What is the constant of variation in a direct variation equation?

Back

The constant of variation (k) is the ratio of y to x in the equation y = kx. It remains constant for all values of x and y.

Front

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

Back

A relationship is a direct variation if it can be expressed in the form y = kx, where k is a non-zero constant, and it passes through the origin.

Front

If y varies directly with x and y = 10 when x = 2, what is y when x = 5?

Back

First, find k: k = y/x = 10/2 = 5. Then, y = kx = 5 * 5 = 25.

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) with a slope equal to the constant of variation k.