Direct variation and slopes

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 as x, what is the constant of variation if y = 6 when x = 27?

Back

k = y/x = 6/27 = 2/9.

Front

How do you find y when x = 2 if y varies directly as x and k = 2/9?

Back

y = kx = (2/9)(2) = 4/9.

Front

What is the formula for direct variation?

Back

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

Front

If y = 14 when x = 6, what is the equation of the direct variation?

Back

y = (14/6)x = (7/3)x.

Front

What does it mean if a graph passes through the origin?

Back

If a graph passes through the origin, it indicates a direct variation between the variables.

Front

Which of the following represents a direct variation: y = 3x + 2 or y = 5x?

Back

y = 5x represents a direct variation because it can be expressed in the form y = kx.

Front

Is the relationship y = 2x - 1 a direct variation?

Back

No, because it does not pass through the origin.

Front

What is the slope of a line in a direct variation?

Back

The slope of a line in a direct variation is equal to the constant of variation (k).

Front

If y varies directly as x and y = 9 when x = 3, what is y when x = 6?

Back

y = kx; k = 9/3 = 3; y = 3(6) = 18.