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 the constant of proportionality.

Front

What is the constant of proportionality (k) in direct variation?

Back

The constant of proportionality (k) is the constant factor that relates the two variables in a direct variation. It can be found by dividing y by x (k = y/x).

Front

If y varies directly with x, and k = 3, what is the equation of the variation?

Back

The equation of the variation is y = 3x.

Front

How do you determine if a relationship is a direct variation?

Back

A relationship is a direct variation if it can be expressed in the form y = kx, where k is a non-zero constant, and the ratio y/x is constant.

Front

What does it mean if k = 0 in a direct variation?

Back

If k = 0, it means that y is always 0 regardless of the value of x, indicating no variation.

Front

If Hayden reads 12 pages in 4 minutes, how many pages can he read in 17 minutes?

Back

Hayden can read 51 pages in 17 minutes.

Front

If the mass of a substance varies directly with its volume, what is the relationship between mass and volume?

Back

The relationship is expressed as mass = k * volume, where k is the constant of proportionality.

Front

What is the value of k if the volume of 100 kg of a substance is 80 liters?

Back

k = 100 kg / 80 liters = 1.25 kg/liter.

Front

If y = 2x, what is the value of y when x = 5?

Back

y = 2 * 5 = 10.

Front

What is the graph of a direct variation relationship?

Back

The graph of a direct variation relationship is a straight line that passes through the origin (0,0).