Direct Variation Flashcard

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 a non-zero constant.

Front

If y varies directly with x, what is the equation that represents this relationship?

Back

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

Front

How do you find the constant of variation (k) in direct variation?

Back

To find k, use the formula k = y/x, where y is the value of the dependent variable and x is the value of the independent variable.

Front

If y = 12 when x = 3, what is the constant of variation (k)?

Back

k = y/x = 12/3 = 4.

Front

If y varies directly with x and k = 4, what is the value of y when x = 6?

Back

y = kx = 4 * 6 = 24.

Front

Which of the following represents direct variation? y = kx, y = k/x, y = x/k, y = mx + b

Back

y = kx.

Front

If y = 22.5 when x = 15, what is the value of y when x = 20?

Back

First, find k: k = y/x = 22.5/15 = 1.5. Then, y = kx = 1.5 * 20 = 30.

Front

The width of a rectangle varies directly with its length. If the width is 6 when the length is 24, what is the equation that shows the relationship?

Back

y = 0.25x, where y is the width and x is the length.

Front

If y varies directly with x, and y is 84 when x is 16, what is the equation representing this situation?

Back

y = \frac{21}{4}x.

Front

What is the graphical representation of direct variation?

Back

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