Question

The graph below represents which system of inequalities?

A)y > 2x − 3
y > −x − 3

B)y < 2x − 2
y < −x + 3

C)y ≤ 2x − 2
y > −x + 3

None of the above

Answer 1

y ≤ 2x -2 Option C.

Explanation:

Equation of the dotted line which passes through (3,0) and (0,8) will be

y = mx+C

m =
`(y-y')/(x-x')=(3-0)/(0-3)` = -1

and C = 3

So equation will be y = x + 3

But shaded blue part is above the dotted line so inequality will be y> -x +3

Equation of the second solid line which passes through ( 0,-2) and (1,0) will be

y = mx + C

m =
`(y-y')/(x-x')` =
`(0+2)/(1-0)` = 2

and C = -2

So equation of the line will be y = 2x - 2

But shaded yellow part is below the solid line.

So inequality will be

y ≤ 2x -2

Option C. is the answer.