Unique Solution of a Linear Equation
A linear equation is an equation in which the highest power of the variable is 1. The general form of a linear equation in two variables, x and y, is given by:
ax + by = c
where a, b, and c are constants.

When we graph a linear equation in two variables, it represents a straight line on the coordinate plane. The solution to a linear equation represents the point where the line intersects the x and y axes.

In the given equation, 2x + 5y = 7, we need to determine the conditions under which it has a unique solution.

Rational Numbers:
Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. Rational numbers include integers, fractions, and terminating or repeating decimals. Since both x and y can take any rational number value, the equation can have infinitely many solutions. Therefore, option 'a' is incorrect.

Real Numbers:
Real numbers include both rational and irrational numbers. They can be expressed as decimals that may or may not terminate or repeat. Similar to the previous case, since both x and y can take any real number value, the equation can have infinitely many solutions. Therefore, option 'b' is also incorrect.

Natural Numbers:
Natural numbers are positive integers starting from 1. Since the equation involves both multiplication and addition, the values of x and y must be such that they satisfy the equation. In this case, the equation has a unique solution when x and y are natural numbers. Therefore, option 'c' is correct.

Positive Real Numbers:
Positive real numbers are real numbers that are greater than zero. Similar to the previous cases, since both x and y can take any positive real number value, the equation can have infinitely many solutions. Therefore, option 'd' is incorrect.

Conclusion:
The equation 2x + 5y = 7 has a unique solution when x and y are natural numbers. This means that there is only one point of intersection between the line represented by the equation and the x and y axes.