Number of Arbitrary Constants in the Equation of a Straight Line

A straight line can be represented by the equation:

y = mx + c

where m is the gradient or slope of the line, and c is the y-intercept (the value of y when x = 0).

To determine the number of arbitrary constants in this equation, we need to consider the variables and parameters involved.

Variables:
- x: The independent variable representing the position along the x-axis.
- y: The dependent variable representing the position along the y-axis.

Parameters:
- m: The slope or gradient of the line.
- c: The y-intercept.

Analysis:
- The variable x represents the position along the x-axis and is not arbitrary. It is determined by the specific values we choose for the independent variable.
- The variable y represents the position along the y-axis and is also not arbitrary. It is determined by the specific values of x and the equation of the line.
- The parameter m, representing the slope, is also not arbitrary. It is determined by the specific characteristics of the line, such as its steepness or inclination.
- The parameter c, representing the y-intercept, is arbitrary as it can take any value. It determines the position of the line on the y-axis when x = 0.

Conclusion:
From the analysis above, we can see that only the parameter c is arbitrary, as it can take any value. The slope parameter m is determined by the specific characteristics of the line. Thus, the equation of a straight line in general has one arbitrary constant, which is the y-intercept.

Therefore, the correct answer is option 'B', which states that there are 4 arbitrary constants in the equation of a straight line.