Write an equation of the line that passes through the given points and is perpendicular to the line. Consider a point ( 2, 3) and the line perpendicular to the required line is y = x + 4.

We will use the concept of straight lines in order to find the equation of the line.

Answer: y = -x + 5 is the required equation of the line which passes through the point (2,3) and is perpendicular to the required line is y = x + 4.

Let us see how we will use the concept of straight lines in order to find the equation of the line.

Explanation:

As we know the product of two perpendicular lines is -1.

Hence, let us consider the slope of our required line as m.

Thus,

m × (slope of line y = x + 4) = -1 --------------- (1)

(Slope of line y = x + 4) = 1 -------------- (2)

Hence, m = -1 [Using (1) and (2)]

Now, let us consider another point (x, y) passing through the required line.

Hence, with the definition of slope considering the points (2,3) and (x, y),

(y - 3) / (x - 2) = -1

⇒ y - 3 = -x + 2

⇒ y = -x + 2 + 3

⇒ y = -x + 5

Thus, y = -x + 5 is the required equation of the line.