Question

Ax+by+c=0 does not represent an equation of line if ____.

A. a=c=0,b≠0
B. b=c=0,a≠0
C. a=b=0
D. c=0,a≠0,b≠0

Answer 1

Option C, where both a and b are zero, does not represent an equation of a line, as it does not define a relationship between the x and y variables necessary to plot such a line on a Cartesian plane.

Step-by-step explanation:

The equation ax+by+c=0 represents a line in two-dimensional space, where a, b, and c are real numbers, and a and b are not both zero. If either a or b, but not both, are zero, the equation still represents a line.

Specifically, if a is zero and b is not zero, this represents a vertical line, whereas if b is zero and a is not zero, it represents a horizontal line. However, option C where a=b=0 does not represent the equation of a line because if both a and b are zero, this no longer defines a line in Cartesian plane.

The equation ax+by+c=0 does not represent an equation of a line if a=c=0 and b≠0. This is because if a=c=0, then the equation becomes 0x+by+0=0 which simplifies to by=0. If b≠0, then the equation by=0 does not represent a line.