Question

Equation of line perpendicular to x + y = 8 is [ ]

a) 2x – y = 4
b) x – y = 2
c) x + y = 11
d) x – 2y = 7​

Answer 1

Answer:

$\large\boxed{\sf{(b)\;x-y=2}}$

Step-by-step explanation:

Given a line having equation,

$x + y = 8$

To find the equation of a line perpendicular to it, we must find its slope.

Therefore, differentiate the given eqn wrt x,

$= > 1 + \dfrac{dy}{dx} = 0 \\ \\ = > \dfrac{dy}{dx} = - 1$

Now, We know that, product of slopes of two perpendicular lines is -1.

Let the slope of required line is m.

Therefore, we will get,

$= > m \times - 1 = - 1 \\ \\ = >m = 1$

Therefore, for the desired line, it's slope should be equal to 1.

Let's check the options.

(a) 2x - y = 4

Differentiating both sides wrt x , we get,

$= > 2 - \dfrac{dy}{dx} = 0 \\ \\ = > \dfrac{dy}{dx} = 2$

Therefore, its not the required line.

(b) x - y = 2

Differentiating both sides wrt x, we get,

$= > 1 - \dfrac{dy}{dx} = 0 \\ \\ = > \dfrac{dy}{dx} = 1$

Therefore, it satisfies the required condition.

Hence, the line perpendicular to the given line will be (b) x - y = 2.