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 in a direct variation equation?

Back

The constant of proportionality (k) is the constant factor that relates the two variables in a direct variation. It represents the ratio of y to x.

Front

If y varies directly with x and y = 12 when x = 3, how do you find the constant of proportionality?

Back

To find the constant of proportionality (k), use the formula k = y/x. Here, k = 12/3 = 4.

Front

How do you determine the value of y when x is given in a direct variation?

Back

To find the value of y when x is given, use the equation y = kx, where k is the constant of proportionality.

Front

What does it mean if a graph does not pass through the origin in relation to direct variation?

Back

If a graph does not pass through the origin, it does not represent a direct variation relationship, even if it is a straight line.

Front

If y varies directly with x and y = 10 when x = 5, what is the value of x when y = 20?

Back

To find x when y = 20, first find k: k = 10/5 = 2. Then use y = kx: 20 = 2x, so x = 10.

Front

What is the equation of direct variation when the constant of proportionality is 3?

Back

The equation of direct variation with a constant of proportionality of 3 is y = 3x.

Front

How can you express a direct variation relationship in terms of an equation?

Back

A direct variation relationship can be expressed in the form y = kx, where k is the constant of proportionality.

Front

If y = 16 when x = 32 in a direct variation, what is the equation representing this situation?

Back

To find the equation, first find k: k = 16/32 = 1/2. The equation is y = (1/2)x.

Front

What is the relationship between x and y in a direct variation?

Back

In a direct variation, as one variable increases, the other variable also increases proportionally, and vice versa.