Question

The shaded region is represented by the inequality:

(a) y – 2x ≤ –1

(b) x – 2y ≤ –1

(c) y – 2x ≥ –1

(d) x – 2y ≥ –1

Answer 1

Correct option is (a) y – 2x ≤ –1

The equation of the line is given as 

y − 2x = −1

Now the shading is away from the origin.

Hence, at y = 0 and x = 0 the inequality is not true.

we know

0 > −1

Hence at origin, the inequality must be of the type 

0 < −1 ....(since inequality is not true at origin).

Hence y − 2x < −1

Also the points on the line is a part of the inequality.

Hence

y − 2x ≤ −1