Explanation:

The equation in the form of y = kx represents a linear relationship between two variables, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality. This equation is known as the slope-intercept form.

Understanding the Equation:
- The equation y = kx implies that the value of y is directly proportional to the value of x.
- The constant k determines the rate of change or slope of the line.

Passing Through the Origin:
When k is equal to zero, the equation becomes y = 0x, which simplifies to y = 0. This means that the value of y is always zero, regardless of the value of x. In other words, the line is a horizontal line passing through the y-axis at y = 0.

Interpretation:
As the constant of proportionality is zero, it implies that there is no change in the value of y with respect to x. Thus, the line passes through the origin (0,0), where both x and y have zero values.

Graphical Representation:
When we plot the graph of y = kx, we can observe that the line always passes through the origin. This is because when x = 0, y = 0, and when x ≠ 0, y ≠ 0. The line starts at the origin and extends infinitely in both the positive and negative directions.

Conclusion:
The equation y = kx always passes through the origin because when the constant of proportionality, k, is zero, the value of y becomes zero regardless of the value of x. The line represents a linear relationship where y is directly proportional to x. When x has a value of zero, y also has a value of zero, resulting in the line passing through the origin (0,0) on the coordinate plane.

The graph of a proportional relationship is a straight line that passes through the origin.Proportional quantities can be described by the equation y = kx, where k is a constant ratio.