Answer:
The correct option is 2.
Step-by-step explanation:
From the given graph it is clear that the y-intercept of red line is 1 and y-intercept of blue line is 4.
The red line passes through the points (0,1) and (5,0). So, the slope of red line is
[tex]m_R=\frac{0-1}{5-0}=-\frac{1}{5}[/tex]
The blue line passes through the points (-2,0) and (0,4). So, the slope of blue line is
[tex]m_B=\frac{4-0}{0-(-2)}=2[/tex]
The slope intercept form of a line is
[tex]y=mx+b[/tex]
Where m is slope and b is y-intercept.
The y-intercept of red line is 1 and slope is [tex]-\frac{1}{5}[/tex].
[tex]y=-\frac{1}{5}x+1[/tex]
Multiply both sides by 5.
[tex]5y=-x+5[/tex]
Add x on both the sides.
[tex]x+5y=5[/tex]
The related equation of red line is x+5y=5.
The shaded region is above the line and the related line is a solid line, therefore the sign of inequality is ≥. So, the first inequality is
[tex]x+5y\geq 5[/tex]
The y-intercept of blue line is 4 and slope is 2.
[tex]y=2x+4[/tex]
The related equation of blue line is y=2x+4.
The shaded region is below the line and related line is a solid line, therefore the sign of inequality is ≤. So, the second inequality is
[tex]y\leq 2x+4[/tex]
Therefore the correct option is 2.
