Answer:
Explanation:
To determine whether each equation shows direct variation, inverse variation, or neither, we can examine the structure of the equation and compare it to the general forms of direct and inverse variation.
Direct Variation: A direct variation equation is of the form y = kx, where k is a constant. This means that y and x are directly proportional to each other.
Inverse Variation: An inverse variation equation is of the form y = k/x or xy = k, where k is a constant. This means that y and x are inversely proportional to each other.
a) y = 6x: This equation is in the form of direct variation, y = kx, where k = 6. Answer: Direct variation.
b) y = 2/x: This equation is in the form of inverse variation, y = k/x, where k = 2. Answer: Inverse variation.
c) y = x - 1: This equation does not fit the forms of either direct or inverse variation. It represents a linear relationship where y and x are not directly or inversely proportional. Answer: Neither direct nor inverse variation.
d) y - 2 = x: This equation represents a linear relationship where y and x are not directly or inversely proportional. Answer: Neither direct nor inverse variation.
e) xy = 7: This equation is in the form of inverse variation, xy = k, where k = 7. Answer: Inverse variation.
f) 5y = x: This equation is in the form of direct variation, y = kx, where k = 1/5. Answer: Direct variation.
Shortcut: To quickly identify direct variation, look for an equation in the form y = kx, where k is a constant. For inverse variation, look for an equation in the form y = k/x or xy = k, where k is a constant. If the equation does not fit these forms, it represents neither direct nor inverse variation.