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

Answer:

y ≤ 2x -2 Option C.

Step-by-step explanation:

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

y = mx+C

m = $\frac{y-y'}{x-x'}=\frac{3-0}{0-3}$ = -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 = $\frac{y-y'}{x-x'}$ = $\frac{0+2}{1-0}$ = 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.