The differential equation that represents the family of lines parallel to $x+y = 2 $ is :

$\frac{dy}{dx}+1=0$

The correct answer is Option (3) → $\frac{dy}{dx}+1=0$

for lines to be parallel, the slope should be same.

$∴x+y=2$

Differentiating w.r.t. 'x'

$1+\frac{dy}{dx}=0$

$∴\frac{dy}{dx}+1=0$ is the differentiate equation that represents the family of curves which are parallel.