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 :)