Identify the equation of a line perpendicular to the line x/2 + y = -1

The correct answer is: y - 2x = 0

Step-by-step solution:-
x/2 + y = -1
∴ y = -1 - x/2
i.e. Y = -1/2 x - 1
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -1/2 …...................................................................... (Equation i)
Now, we know that slopes of perpendicular lines are negative reciprocals of each other.
∴ Slope of line perpendicular to the given line = -1/ slope of given line
∴ Slope of line perpendicular to the given line = -1/ -1/2
∴ Slope of line perpendicular to the given line = 2
∴ We need to find the line from the given options, whose slope = 2.
a. y = -1/2 x
∴ y = -1/2 x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -1/2 ≠ 2
b. y = -x
∴ y = - x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -1 ≠ 2
c. y - 2x = 0
∴ y = 2x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = 2
d. y + 2x = 0
∴ y = -2x + 0
Comparing the above equation with standard form of a line i.e. y = mx + c, we get-
m = -2 ≠ 2
Final Answer:-
∴ Option c i.e. y - 2x = 0 is the correct option.