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 a non-zero constant.

Front

What is the equation of direct variation?

Back

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

Front

If y varies directly with x and k = 3, what is the equation?

Back

y = 3x

Front

What does the constant k represent in direct variation?

Back

The constant k represents the rate of change or the slope of the line in a direct variation.

Front

Which of the following is a direct variation equation: y = 5x or y = 5x + 2?

Back

y = 5x is a direct variation equation.

Front

If y = 4 when x = 2, what is the constant of variation k?

Back

k = 2 (since y = kx, 4 = k(2) => k = 4/2 = 2).

Front

Is the equation y = 3x - 1 a direct variation equation?

Back

No, it is not a direct variation equation because it has a constant term (-1).

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).

Front

If y varies directly with x and y = 10 when x = 5, what is the value of y when x = 10?

Back

y = 20 (since k = 2, y = 2(10) = 20).

Front

What is another name for the slope in the context of direct variation?

Back

The slope is also referred to as the constant of variation (k).