Answer:
[tex]y<4x-5[/tex]
[tex]y\leq 2x+3[/tex]
Step-by-step explanation:
step 1
Find the equation of the solid line
From the graph take the points (0,3) and (4,11)
Find the slope
[tex]m=(11-3)/(4-0)\\m=8/4=2[/tex]
The equation of the solid line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2[/tex]
[tex]b=3[/tex] ----> the y-intercept is the point (0,3)
substitute
[tex]y=2x+3[/tex]
therefore
The inequality is
[tex]y\leq 2x+3[/tex]
step 2
Find the equation of the dashed line
The slope is given
[tex]m=4[/tex]
From the graph take the y-intercept (0,-5)
The equation of the solid line in slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=4[/tex]
[tex]b=-5[/tex]
substitute
[tex]y=4x-5[/tex]
therefore
The inequality is
[tex]y<4x-5[/tex]
because the shaded region is below the dashed line
therefore
The system of inequalities is
[tex]y<4x-5[/tex]
[tex]y\leq 2x+3[/tex]
