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

If y varies directly with x, and y = 39 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 39/3 = 13.

Front

If y = kx and k = 5, what is the value of y when x = 10?

Back

y = 5 * 10 = 50.

Front

How do you find the value of y when x = 2 if y varies directly with x and y = 39 when x = 3?

Back

First, find k: k = 39/3 = 13. Then, y = k * 2 = 13 * 2 = 26.

Front

In a direct variation, if you earn $70 for 5 hours of work, how much do you earn for 22 hours?

Back

Set up the proportion: (70/5) = (x/22). Solve for x: x = (70/5) * 22 = 308.

Front

What is the formula to calculate direct variation?

Back

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

Front

If Daniel received $55.35 in interest on $1230, how much interest would he receive on $2000?

Back

Set up the proportion: (55.35/1230) = (x/2000). Solve for x: x = (55.35/1230) * 2000 = 90.

Front

What does it mean if two quantities vary directly?

Back

It means that as one quantity increases, the other quantity increases at a constant rate.

Front

If Trina earns $187.15 for 19 hours of work, how much will she earn for 40 hours?

Back

Set up the proportion: (187.15/19) = (x/40). Solve for x: x = (187.15/19) * 40 = 394.

Front

What is the relationship between the variables in a direct variation?

Back

The relationship is linear, meaning that a graph of the two variables will form a straight line through the origin.