Question

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

- y = - x
- y = - x
- y - 2x = 0
- y + 2x = 0

## The correct answer is: y - 2x = 0

### Hint:-

1. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates. Slope = m = rise / run = y2-y1 / x2-x1

2. Slopes of perpendicular lines are negative reciprocals of each other.

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 = - …...................................................................... (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/ -

∴ Slope of line perpendicular to the given line = 2

∴ We need to find the line from the given options, whose slope = 2.

a. y = - x

∴ y = - x + 0

Comparing the above equation with standard form of a line i.e. y = mx + c, we get-

m = - ≠ 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.

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