The equation of the straight line which passes through the point ${(1, 2)}$ and cuts off equal intercepts from axes, is
A) $x + y = 1$
B) $x - y = 1$
C) $x + y + 1 = 0$
D) $x - y - 2 = 0$

Hint: In this question we have to find the equation of line which intercept equally on both axes. As intercept is given in this question therefore equation of the intercept form of straight line will be used in this question. Point which passes through a particular point must satisfy the equation of the line.

Formula used: In this question equation of intercept form of straight line is used :
$\dfrac{x}{a} + \dfrac{y}{b} = 1$
Where, a and b are intercept of x and y axis respectively.

Complete step by step solution: Given: A straight line passing through the point ${(1, 2)}$ and have equal intercepts.

The equation of intercept form of straight line is
$\dfrac{x}{a} + \dfrac{y}{b} = 1$
a is x intercept and b is y intercept
According to question intercept are equal $a = b$
Now,
$\dfrac{x}{a} + \dfrac{y}{a} = 1$
$x + y = a$
Coordinates of a point is represent as ${(x, y)}$
It is given in question that straight line is passes through point ${(1, 2)}$
$x = 1$
$y = - 2$
The point which passes through a straight line must satisfy the equation of line.
$x + y = a$
$1 - 2 = a$
$a = - 1$
Now equation of line is
$x + y = - 1$
$x + y + 1 = 0$

Thus, Option (C) is correct.

Note: Do not use the equation of line in any other form because it will become very difficult to find the equation of lines and sometimes one may not find the equation of line by using the general equation of lines. If in any question an intercept on line is given then use only the intercept form of the straight line equation.