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 does the slope represent in a direct variation equation?

Back

The slope (k) in a direct variation equation y = kx represents the rate of change of y with respect to x.

Front

How do you identify a direct variation from an equation?

Back

An equation represents direct variation if it can be written in the form y = kx, where k is a non-zero constant.

Front

What is the slope of the line represented by the equation y = 3x?

Back

The slope of the line is 3.

Front

What is the slope of the line represented by the equation y = -5x?

Back

The slope of the line is -5.

Front

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

Back

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

Front

If y = rac{1}{2}x, what is the value of y when x = 8?

Back

y = 4, since y = rac{1}{2}(8) = 4.

Front

What is the equation of a line that passes through the origin with a slope of 4?

Back

The equation is y = 4x.

Front

Is the equation y = -rac{3}{4}x a direct variation?

Back

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

Front

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

Back

In direct variation, as x increases, y increases proportionally, and as x decreases, y decreases proportionally.