Chapter 5 Direct Variation and Proportions

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 in the form y = kx, where k is a non-zero constant.

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

If y = 2x, is this a direct variation?

Back

Yes, because it can be expressed in the form y = kx with k = 2.

Front

What does the slope represent in a graph?

Back

The slope represents the rate of change of y with respect to x, indicating how much y changes for a unit change in x.

Front

What is the slope of the line represented by the equation y = 3x?

Back

The slope is 3.

Front

If y = 1/4x, what is the constant of variation?

Back

The constant of variation is 1/4.

Front

How do you find the constant of variation from a direct variation problem?

Back

To find the constant of variation, divide y by x (k = y/x) for any point (x, y) on the line.

Front

What is the relationship between hours worked and money earned in direct variation?

Back

In direct variation, the amount of money earned is directly proportional to the number of hours worked.

Front

If $70 is earned in 5 hours, how much is earned in 22 hours?

Back

$308.

Front

What is the formula to calculate the slope from two points (x1, y1) and (x2, y2)?

Back

The formula is slope (m) = (y2 - y1) / (x2 - x1).