Answer:
C.
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (0, -2) and (6, 7).
(0, -2) → b = -2
Calculate the slope:
[tex]m=\dfrac{7-(-2)}{6-0}=\dfrac{9}{6}=\dfrac{9:3}{6:3}=\dfrac{3}{2}[/tex]
Put the value of b and m to the equation of the line in the slope-intercept form:
[tex]y=\dfrac{3}{2}x-2[/tex]
=====================================
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
======================================
We have the soli line (≤ or ≥).
Shaded region is above the line (> or ≥)
Therefore we have the answer: [tex]y\geq\dfrac{3}{2}x-2[/tex]
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y\geq\dfrac{3}{2}x-2[/tex] multiply both sides by 2
[tex]2y\geq3x-4[/tex] subtract 3x from both sides
[tex]-3x+2y\geq-4[/tex] change the signs
[tex]3x-2yleq4[/tex]
