Answer:
C. 2x-y>-7
Step-by-step explanation:
The Line is not part of the region since is drawn in the graph using a dotted line, but we still need to find its equation.
The equation of a line is y=mx+b, where 'm' is the slope.
'm' can be obtained using the following formula.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
To find the slope, as well 'b' we need points from the line, those will be (-6,-5), (0,7) as (x2,y2) and (x1,y1) respectively
Evaluating those point in the formula we have 'm' =2
Using now the above result and the point (0,7) in the equation y=mx+b, we obtain the value for 'b'.
7=2*0+b7
b=7
Hence our line is y=2x+7, and if we write it in standard form we obtain the following> y-2x=7.
Now, since our line is not part of the region, and the region is below that line, there is the < sign.
Hence the inequality that corresponds to the figure is y-2x<7 or, if we multiply by -1 (changin orientation of signs) 2x-y>-7
