Algebra IA - 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 direct variation?

Back

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

Front

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

Back

y = 4x

Front

What ordered pair does a direct variation always pass through when graphed?

Back

(0, 0)

Front

In a direct variation, if y = 20 when x = 5, what is the value of y when x = 10?

Back

y = 40

Front

Write the equation for the direct variation if k = 2.

Back

y = 2x

Front

If y = 15 when x = 3, what is the constant of proportionality?

Back

k = 5

Front

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

Back

To find k, divide y by x (k = y/x).

Front

If y varies directly with x and y = 30 when x = 6, what is y when x = 2?

Back

y = 10

Front

What is the graph of a direct variation equation like?

Back

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