Nov 6 - Bellwork (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 in the form y = kx, where k is the constant of variation.

Front

How can you identify if two variables show direct variation?

Back

To identify if two variables show direct variation, check if the ratio of y to x is constant for all pairs of values. If it is, then y varies directly with x.

Front

What does the constant of variation represent in a direct variation equation?

Back

The constant of variation (k) represents the factor by which one variable changes in relation to another. It indicates how much y changes for a unit change in x.

Front

Is the equation y = x^2 an example of direct variation? Why or why not?

Back

No, the equation y = x^2 is not an example of direct variation because the ratio of y to x is not constant; it changes as x changes.

Front

What is the constant of variation in the equation y = 9.50x?

Back

The constant of variation is 9.50, which means that for each movie ticket purchased, Marty pays $9.50.

Front

If y = 5x, does this represent a direct variation?

Back

Yes, this represents a direct variation because it can be expressed in the form y = kx, where k = 5.

Front

What is the relationship between direct variation and proportionality?

Back

Direct variation implies proportionality; if y varies directly with x, then y is proportional to x, meaning y/x = k is constant.

Front

Can a relationship be considered direct variation if the constant of variation is negative?

Back

Yes, a relationship can still be considered direct variation if the constant of variation is negative; it simply indicates that as one variable increases, the other decreases.

Front

What is the general form of a direct variation equation?

Back

The general form of a direct variation equation is y = kx, where k is the constant of variation.

Front

How do you find the constant of variation from a set of values?

Back

To find the constant of variation, divide the value of y by the corresponding value of x (k = y/x) for any pair of values.