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 two quantities vary directly?

Back

If two quantities vary directly, it means that as one quantity increases, the other quantity increases at a constant rate, and vice versa.

Front

How do you find the constant of variation (k)?

Back

To find the constant of variation (k), divide the value of y by the value of x in the equation y = kx.

Front

If y = 3x, what is the constant of variation?

Back

The constant of variation (k) is 3.

Front

If a worker earns $150 for 10 hours of work, how much will they earn for 25 hours?

Back

$375 (Using direct variation: k = 150/10 = 15; so for 25 hours: y = 15 * 25 = 375).

Front

What is the equation for a direct variation if y varies directly with x and k = 2?

Back

y = 2x.

Front

If y = 5 when x = 1, what is the equation of the direct variation?

Back

y = 5x.

Front

In a direct variation, if x doubles, what happens to y?

Back

y also doubles.

Front

If a car travels 60 miles in 1 hour, how far will it travel in 4 hours?

Back

240 miles (Direct variation: k = 60; so for 4 hours: y = 60 * 4 = 240).

Front

What is the formula to calculate the amount earned based on hours worked in direct variation?

Back

Amount Earned = Rate per Hour * Hours Worked.