Question

Equation of a line passing through the intersection of the lines x − y = 3 and x + y = 0 with inclination 45° is ______.

पर्याय

• x + y = 3

• x − y = 3

• y − x = 3

• y = 3x + 1

Answer 1

Equation of a line passing through the intersection of the lines x − y = 3 and x + y = 0 with inclination 45° is x − y = 3.

Explantion:

Given,

Equations:

⇒ x − y = 3 ........(1)

⇒ x + y = 0 ........(2)

Adding equation (1) and (2), we get:

⇒ (x − y) + (x + y) = 3 + 0

⇒ x + x − y + y = 3

⇒ 2x = 3

⇒ x = `3/2`

Substituting value of x in equation (2), we get:

⇒ `3/2`​ + y = 0

⇒ y = `−3/2`

∴ Point of intersection of lines x − y = 3 and x + y = 0 is `(3/2,−3/2)`

Given,

Inclination (θ) = 45°

Slope = tan 45° = 1.

By point-slope form,

Equation of line: y − y₁ = m(x − x₁)

Equation of line passing through `(3/2,−3/2)` and slope = 1 is:

⇒ `y−(−3/2​)=1(x−3/2​)`

⇒ `y + 3/2 ​= x − 3/2​`

⇒ `x − y = 3/2​ + 3/2​`

⇒ `x − y = 6/2​`

⇒ x − y = 3