In economics, if a diagram has a line passing through the origin and h

In economics, if a diagram has a line passing through the origin and has 45° angle with either axis and it is asserted that along the line X = Y, what is tacitly assumed?

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Both variables are pure numbers.

Both variables are in the same unit.

Both variables are in different units.

At least one variable is a pure number.

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CDS-1 – 2020

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In a standard two-dimensional Cartesian coordinate system, a line passing through the origin (0,0) has the equation Y = mX, where m is the slope. If the angle with the X-axis (or Y-axis) is 45°, the slope m = tan(45°) = 1. Thus, the equation of the line is Y = X. For the numerical values of X and Y to be equal and represented by a 45° line through the origin, the scales used on the X-axis and the Y-axis must be the same. This implies that the units of measurement for X and Y, or at least their graphical representation on the axes, are comparable such that equal distances along each axis represent equal changes in the variable’s value. In economic diagrams, this often means the variables are in the same unit (e.g., both in Rupees, both in quantity units) or scaled identically.

– A 45° line through the origin in a 2D graph represents the relationship Y=X.
– For Y=X to be accurately represented by a 45° line, the scales on the X and Y axes must be identical.
– This identical scaling is usually interpreted as the variables being in the same unit or having their values measured on the same scale.

If the scales on the axes were different, a line representing Y=X would not necessarily be 45°. For example, if the Y-axis was scaled twice as densely as the X-axis, the line Y=X would appear flatter than 45°. Conversely, if the X-axis was scaled twice as densely, the line would appear steeper.

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