Question

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

Answer 1

Answer:

Option A

$y\geq -3x+2$

$y\leq x-3$

Step-by-step 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

$y\geq -3x+2$

$y\leq x-3$