8.5E Direct Variation Homework

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, what does that imply about their relationship?

Back

It implies that as x increases, y increases proportionally, and as x decreases, y decreases proportionally.

Front

How do you find the constant of variation (k) in a direct variation problem?

Back

To find k, divide y by x (k = y/x) using any pair of corresponding values.

Front

In the equation y = kx, what does k represent?

Back

k represents the constant of variation, indicating how much y changes for a unit change in x.

Front

If 15 miles is represented by 3 centimeters on a map, how do you find the scale factor?

Back

The scale factor is found by dividing the actual distance by the scaled distance: Scale Factor = 15 miles / 3 cm = 5 miles/cm.

Front

Using the scale factor, how many centimeters represent 135 miles?

Back

To find the centimeters for 135 miles, divide 135 miles by the scale factor: 135 miles / 5 miles/cm = 27 cm.

Front

What is the formula to calculate interest in a direct variation scenario?

Back

Interest = k * Principal, where k is the rate of interest.

Front

If Daniel received $55.35 in interest for $1230, how do you find the interest rate?

Back

Interest Rate (k) = Interest / Principal = $55.35 / $1230 = 0.045 or 4.5%.

Front

How do you calculate the interest for a different principal amount using direct variation?

Back

Use the formula: Interest = k * New Principal, where k is the constant found from previous data.

Front

If a person with a mass of 90 kg contains 60 kg of water, how do you find the water mass for a different mass?

Back

Use the ratio: Water Mass = (Water Mass for 90 kg / 90 kg) * New Mass.