Question

The differential equation of all non-vertical lines in a plane is

• A. \( \frac{dy}{dx} = 0 \)
• B. \( \frac{dx}{dy} = 0 \)
• C. \( \frac{dz}{dx} = 0 \)
• D. \( \frac{dz}{dy} = 0 \)

Hint:

For any non-vertical line, the slope \( \frac{dy}{dx} \) is constant, and this is reflected in the differential equation. Vertical lines do not satisfy this equation, as their slope is undefined.

Answer 1

The Correct Option is A

The differential equation of a line is derived from its slope. For a non-vertical line (which is a line that is not parallel to the y-axis), the slope is constant and can be represented as the derivative of \( y \) with respect to \( x \). The equation for the slope of a line is: \[ \frac{dy}{dx} = \text{constant} \] For a non-vertical line in a plane, the slope is finite and thus not zero. This condition results in a simple differential equation. Therefore, the correct equation for non-vertical lines is: \[ \frac{dy}{dx} = 0 \] This is the general form of the differential equation that represents all non-vertical lines in the plane.