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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

20 POINTS HELP PLEASE Which system of inequalities is represented by the graph photo attached below A y gt 3x2 yltx3 B ylt 3x2 ygt x 3 C ylt 3x2 yltx3 D ygt3x2 class=

Respuesta :

calculista

Answer:

Option A

[tex]y\geq -3x+2[/tex]

[tex]y\leq x-3[/tex]

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

[tex]m=(-1-2)/(1-0)=-3[/tex]

The equation in slope intercept form is equal to

[tex]y=-3x+2[/tex]

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

so

The inequality is

[tex]y\geq -3x+2[/tex] ----> 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

[tex]m=(0+3)/(3-0)=1[/tex]

The equation in slope intercept form is equal to

[tex]y=x-3[/tex]

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

so

The inequality is

[tex]y\leq x-3[/tex] ----> inequality B

therefore

The system of inequalities is

[tex]y\geq -3x+2[/tex]

[tex]y\leq x-3[/tex]

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