The inequality that represents the graph in the box is
[tex]y>-3x+6[/tex]
Given :
The graph of the linear inequality
Lets pick two points from the graph to frame the linear equation
Slope intercept form of the equation is
[tex]y=mx+b[/tex]
Where m is the slope and b is the y intercept
y intercept is (0,6) from the graph
so b=6
Now we find out slope m using formula
Pick two points (0,6) and (2,0)
[tex]slope = \frac{y_2-y_1}{x_2-x_1} \\m=\frac{0-6}{2-0} =-3[/tex]
m=-3
So the equation is [tex]y=-3x+6[/tex]
Now we check the inequality sign by testing any point on shaded area
lets pick (4,0)
lets plug in 4 for x and 0 for y
[tex]y=-3x+6\\0=-3(4)+6\\\\0=-6\\0>-6[/tex]
The inequality for the given graph is
[tex]y>-3x+6[/tex]
we cannot use >= sign because we have dotted lines
Learn more : brainly.com/question/17203372
