Direct Variation (shorter)

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 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

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the ratio of y to x in the equation y = kx. It remains constant for all values of x and y.

Front

If y varies directly with x, what is the value of y when x = 0?

Back

If y varies directly with x, then y = 0 when x = 0.

Front

How do you find the constant of variation from a word problem?

Back

To find the constant of variation, divide the value of y by the value of x (k = y/x) for any pair of values.

Front

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

Back

A direct variation always goes through the ordered pair (0, 0).

Front

If a dishwasher uses 65 gallons of water to wash 5 loads, what is the constant of variation?

Back

k = 13 (calculated as 65 gallons / 5 loads).

Front

If y = -20 when x = 3, what is y when x = 15 in direct variation?

Back

y = -100 (calculated using the constant of variation).

Front

If y = 16 when x = 32, what is y when x = -60 in direct variation?

Back

y = -30 (calculated using the constant of variation).

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx.