Maths-

General

Easy

Question

# Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.Application

Hint:

### 1. Slope of verticle lines are undefined & slop of horizontal lines are 0.

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

3. Equation of a line in slope point form is-

(y-y1) = m (x-x1)

## The correct answer is: ∴ Equation of the given line is y = -9.

### Step-by-step solution:-

Let l be the line for which slope is to be found.

The given equation of line x = 5 represents a verticle line (because its y-coordinate = 0)

Now, line l is perpendicular to the given line (x = 5).

∴ line l is a horizontal line i.e. parallel to x-axis.

Slope of a horizontal line i.e. parallel to x-axis is always 0

∴ Slope of line l = m = 0 …...................................................................................................... (Equation i)

We are given that line l passes through the point (2,-9) and we know its slope.

i.e. x1 = 2 & y1 = -9 & m = 0

We can use slope point form of an equation to find the equation of line l-

(y - y1) = m (x-x1)

∴ [y - (-9)] = 0 (x-2)

∴ y + 9 = 0

∴ y = -9

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