Question

20 POINTS!!!! HELP PLEASE! Which system of inequalities is represented by the graph (photo attached) below?

A
y >= -3x+2
y<=x-3

B
y<= -3x+2
y>= x -3

C
y<= -3x+2
y<=x-3

D
y>-3x+2
y

Answer 1

Option A

`y\geq -3x+2`

`y\leq x-3`

Explanation:

step 1

Find the equation of the inequality A (solid line with negative slope)

we have the points

(0,2) and (1,-1)

The slope is

`m=(-1-2)/(1-0)=-3`

The equation in slope intercept form is equal to

`y=-3x+2`

The solution of the inequality is the shaded area above the solid line

so

The inequality is

`y\geq -3x+2` ----> inequality A

step 2

Find the equation of the inequality B (solid line with positive slope)

we have the points

(0,-3) and (3,0)

The slope is

`m=(0+3)/(3-0)=1`

The equation in slope intercept form is equal to

`y=x-3`

The solution of the inequality is the shaded area below the solid line

so

The inequality is

`y\leq x-3` ----> inequality B

therefore

The system of inequalities is

`y\geq -3x+2`

`y\leq x-3`