The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is

Answer is (B)

Slope of the given line y = x is 1.

Thus, slope of line perpendicular to y = x is -1.

Line passes through the point (3, 2).

So, equation of the required line is:y-2=-l (x – 3) => x + y = 5

B. x + y = 5

Explanation:

Given that straight line passing through the point (3, 2)

And perpendicular to the line y = x

Let the equation of line ‘L’ is

y – y₁ = m(x – x₁)

Since, L is passing through the point (3, 2)

∴ y – 2 = m(x – 3) … (i)

Now, given eq. is y = x

Since, the above equation is in y = mx + b form

So, the slope of this equation is 1

It is also given that line L and y = x are perpendicular to each other.

We know that, when two lines are perpendicular, then

m₁ × m₂ = -1

∴ m × 1 = -1

⇒ m = -1

Putting the value of m in equation (i), we get

y – 2 = (-1) (x – 3)

⇒ y – 2 = -x + 3

⇒ x + y = 3 + 2

⇒ x + y = 5

Hence, the correct option is (b)