X − y = 0, is a line passing through the origin as point (0, 0) satisfies the given equation.

X-y=0
x=y
hence if x=0 y =0
which proves that x-y=0 is the line which passes through origin (0, 0)
hence, option A is correct

Line Equation: x−y=0

The given equation is x−y=0. Let's analyze the equation to understand the characteristics of the line represented by it.

1. Standard Form:
The given equation is in the standard form of a linear equation, which is Ax + By = C. In this case, A = 1, B = -1, and C = 0.

2. Slope-Intercept Form:
To determine the slope-intercept form of the equation, we need to isolate y. Let's rearrange the equation:

x - y = 0
-y = -x (subtracting x from both sides)
y = x (dividing by -1)

Now, the equation is in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. In this case, the slope (m) is 1 and the y-intercept (b) is 0. Therefore, the slope-intercept form of the equation is y = x.

3. Characteristics of the Line:

Slope:
The slope of the line is given by the coefficient of x in the slope-intercept form. In this case, the slope is 1. A slope of 1 means that as x increases by 1 unit, y increases by 1 unit. The line has a positive slope, indicating an upward direction from left to right.

Y-Intercept:
The y-intercept is the point where the line intersects the y-axis. In this case, the y-intercept is 0. Therefore, the line passes through the origin (0, 0).

Parallel to Y-Axis:
A line is parallel to the y-axis if its slope is undefined. In this case, the slope is defined and equal to 1. Thus, the line is not parallel to the y-axis.

Parallel to X-Axis:
A line is parallel to the x-axis if its slope is 0. In this case, the slope is 1, not 0. Therefore, the line is not parallel to the x-axis.

Conclusion:
Based on the analysis, the line represented by the equation x−y=0 passes through the origin (0, 0), making option A the correct answer.