Find the equation of a line which passes through (1, 2) and is perpendicular to the line with an equation y = x – 1.

The correct answer is: x + y = 3 is the equation of the given line.

Step-by-step solution:-
Let l be the line for which slope is to be found.
Comparing the equation y = x – 1 with standard form of a straight line i.e. y = mx + c, we get-
m = 1 ….................................................................................................................... (Equation i)
Now, line l is perpendicular to this line (y = x – 1) .............................................. (Given)
and we know that- Slopes of perpendicular lines are negative reciprocals of each other.
∴ Slope of line l = -1 / slope of line (y = x - 1)
∴ Slope of line l = -1 / 1 = -1 ....................... (From Equation i) ............................ (Equation ii)
We are given that line l passes through the point (1,2) and we know its slope.
i.e. x1 = 1 & y1 = 2 & m = -1
We can use slope point form of an equation to find the equation of line l-
(y - y1) = m (x-x1)
∴ (y - 2) = -1 (x-1)
∴ y - 2 = -x + 1
∴ x + y = 1 + 2
∴ x + y = 3
Final Answer:-
∴ x + y = 3 is the equation of the given line.