Proportional Relationships Review

Front

What is a direct variation equation?

Back

A direct variation equation is a linear equation of the form y = kx, where k is a non-zero constant. In this equation, y varies directly with x.

Front

Is y = 2x - 4 a direct variation equation?

Back

No

Front

Is y = -6x a direct variation equation?

Back

Yes

Front

What does it mean for two quantities to be proportional?

Back

Two quantities are proportional if they maintain a constant ratio to each other.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant factor (k) in the equation y = kx that relates the two proportional quantities.

Front

If y varies directly with x, and y = 12 when x = 3, what is the constant of proportionality?

Back

k = 4 (since 12 = k * 3, thus k = 12/3 = 4).

Front

What is the equation of a line that represents a direct variation?

Back

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

Front

If the ratio of y to x is 7:8, what is the constant of proportionality?

Back

k = \frac{7}{8}.

Front

If y = 14 when x = 9, is y directly proportional to x?

Back

Yes, because the ratio \frac{y}{x} = \frac{14}{9} is constant.

Front

What is the relationship between proportional relationships and linear equations?

Back

Proportional relationships can be represented by linear equations that pass through the origin (0,0).