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, expressed as y = kx, where k is a non-zero constant.

Front

What is the constant of variation in direct variation?

Back

The constant of variation (k) is the non-zero constant that relates the two variables in a direct variation equation.

Front

Is the equation y = 3x a direct variation?

Back

Yes, y = 3x is a direct variation because it can be expressed in the form y = kx.

Front

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

Back

(0, 0) - The origin.

Front

If y varies directly with x, and y = 10 when x = 2, what is the constant of variation?

Back

k = 5, because y = kx implies 10 = k(2) => k = 10/2 = 5.

Front

True or False: The bank balance is directly proportional to the amount of saving.

Back

True.

Front

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

Back

y = kx.

Front

What is the graph of a direct variation equation like?

Back

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

Front

If y = 4 when x = 1, what is y when x = 3 in direct variation?

Back

y = 12, because k = 4 and y = kx => y = 4(3) = 12.

Front

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

Back

As x increases, y increases proportionally, and as x decreases, y decreases proportionally.