Respuesta :

gmany

Answer:

[tex]\large\boxed{-3x+2y\geq7}[/tex]

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

====================================

We have solid line (≤, ≥).

Shaded region is above the line (>, ≥)

Therefore, the inequality sign must be: ≥

Finally, your answer is -3x + 2y ≥ 7.

Check the equation of a line.

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we ahve the points (3, 8) and (1, 5) - look at the picture.

Substitute:

[tex]m=\dfrac{5-8}{1-3}=\dfrac{-3}{-2}=\dfrac{3}{2}[/tex]

[tex]y-8=\dfrac{3}{2}(x-3)[/tex]

Convert to the standard form [tex]Ax+By=C[/tex]:

[tex]y-8=\dfrac{3}{2}(x-3)[/tex]            multiply both sides by 2

[tex]2y-16=3(x-3)[/tex]           use the distributive property

[tex]2y-16=3x-9[/tex]             subtract 3x from both sides

[tex]-3x+2y-16=-9[/tex]           add 16 to both sides

[tex]-3x+2y=7[/tex]         CORRECT :)

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