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 variation.

Front

What is the constant of variation in a direct variation equation?

Back

The constant of variation (k) is the non-zero constant 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 = 10 when x = 2, what is the constant of variation?

Back

k = 5 (since k = y/x = 10/2).

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx.

Front

How do you find the value of k in a direct variation problem?

Back

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

Front

If 20 miles is represented by 4 centimeters on a map, how many centimeters represent 100 miles?

Back

20 cm (since 100 miles is 5 times 20 miles, and 5 times 4 cm is 20 cm).

Front

What does the graph of a direct variation look like?

Back

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

Front

If y = 3 when x = 1, what is the equation of the direct variation?

Back

y = 3x.

Front

What is the relationship between the constant of variation and the slope of the line in a direct variation?

Back

In a direct variation, the constant of variation (k) is equal to the slope of the line.

Front

If the constant of variation is 4, what is the value of y when x = 5?

Back

y = 20 (since y = kx = 4 * 5).