Identify the equation of a line parallel to the line y = x – 1

The correct answer is: x = y - 1

Step-by-step solution:-
y = x - 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 1 …...................................................................... (Equation i)
Now, we know that slopes of parallel lines are equal.
∴ Slope of line parallel to the given line = slope of given line
∴ Slope of line perpendicular to the given line = 1
∴ We need to find the line from the given options, whose slope = 1.
a. y = 2x - 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 2 ≠ 1
b. x = y - 1
∴ x + 1 = y
i.e. y = x + 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 1
c. x + y = 1
∴ y = -x + 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -1 ≠ 1
d. y = x + 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 1
Final Answer:-
∴ Option b i.e. x = y - 1 & d i.e. y = x + 1 are both the correct options as both the equations are actually the same.