Question

Determine whether or not the equations represent a direct variation. Sort the equations into the appropriate category.

Direct Variation A. y = 3x B. -0.5x = y
Not Direct Variation C. X=-1 D. y = 2^2x+7

Answer 1

Equations A and B represent direct variation, while equations C and D do not.

Step-by-step explanation:

Direct variation refers to an equation in the form y = kx, where k is a constant. A direct variation equation indicates that as x increases or decreases, y will also increase or decrease in a proportional manner. Let's categorize the given equations:

1. Direct Variation: Equation A, y = 3x, is a direct variation because it fits the form y = kx, where k = 3.
2. Direct Variation: Equation B, -0.5x = y, is also a direct variation because it fits the form y = kx, where k = -0.5.
3. Not Direct Variation: Equation C, x = -1, is not a direct variation because it does not fit the form y = kx. It is a linear equation with a constant value of x.
4. Not Direct Variation: Equation D, y = 2^(2x + 7), is not a direct variation because it does not fit the form y = kx. It is an exponential equation with a variable in the exponent.