Question

What do the following two equations represent?

4x-2y = -5
4x-2y = -5

A) The same line
B) Distinct parallel lines
C) Perpendicular lines
D) Intersecting, but not perpendicular lines.

Answer 1

The two given equations, 4x-2y = -5 and 4x-2y = -5, represent the exact same line, as they have the same coefficients and constant term.

The two equations given, 4x-2y = -5 and 4x-2y = -5, represent the same line. This is because they have identical coefficients for both x and y, as well as the same constant term. Therefore, these equations are just two instances of the same linear equation. A linear equation of the form ax + by = c represents a straight line when graphed on a coordinate plane, and in this case, since both equations are the same, they would graph as the exact same line, not as distinct lines, perpendicular lines, or intersecting lines that are not perpendicular.