Practice 9.1

Front

What does it mean when y varies directly with x?

Back

It means that as x increases, y also increases at a constant rate, represented by the equation y = kx, where k is a constant.

Front

If y = 84 when x = 16, how do you find the constant of variation (k)?

Back

You can find k by rearranging the direct variation equation: k = y/x. Here, k = 84/16 = 5.25.

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx, where k is the constant of variation.

Front

What does it mean when y varies inversely with x?

Back

It means that as x increases, y decreases, and vice versa, represented by the equation y = k/x, where k is a constant.

Front

If y = 150 when x = 2, how do you find y when x = 25 in inverse variation?

Back

Use the equation k = xy. First, find k: k = 150 * 2 = 300. Then, find y when x = 25: y = 300/25 = 12.

Front

What is the equation for inverse variation?

Back

The equation for inverse variation is y = k/x, where k is the constant of variation.

Front

How do you determine the height of a wave that varies directly with time?

Back

Use the direct variation equation: height = k * time. Find k using known values, then solve for unknowns.

Front

If a wave is 6 feet high at 4 seconds, what is the constant of variation (k)?

Back

k = height/time = 6 feet / 4 seconds = 1.5 feet/second.

Front

How do you find the time for a wave to reach a height of 10 feet if it varies directly with time?

Back

Use the equation: height = k * time. Here, 10 = 1.5 * time, so time = 10/1.5 = 6.67 seconds.

Front

What is the difference between direct and inverse variation?

Back

In direct variation, y increases with x; in inverse variation, y decreases as x increases.