Answer:
[tex]\large\boxed{A.\ y\leq-2x+3,\ y\leq x+3}[/tex]
Step-by-step explanation:
<, > - dotted line
≤, ≥ - solid line
<, ≤ - shaded region below the line
>, ≥ - shaded region above the line
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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, 3) - y-intercept → b = 3 (for both lines)
f(x)
(0, 3), (1, 1)
[tex]m=\dfrac{1-3}{1-0}=\dfrac{-2}{1}=-2[/tex]
Substitute:
[tex]f(x):\ y=-2x+3[/tex]
The shaded region is below the solid line. Therefore: [tex]y\leq-2x+3[/tex]
g(x):
(0, 3), (2, 5)
[tex]m=\dfrac{5-3}{2-0}=\dfrac{2}{2}=1[/tex]
Substitute:
[tex]g(x):\ y=1x+3=x+3[/tex]
The shaded region is below the solid line. Therefore: [tex]y\leq x+3[/tex]
