Answer :
Given that the two points are (0,2) and (-3,-7)
We need to determine the linear inequality that represents the graph.
Slope:
The slope can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the coordinates (0,2) and (-3,-7) in the formula, we have;
[tex]m=\frac{-7-2}{-3-0}[/tex]
[tex]m=\frac{-9}{-3}[/tex]
[tex]m=3[/tex]
Thus, the slope is 3.
y - intercept:
The y - intercept is the value of y when x = 0
Thus, from the graph, we can see that the y - intercept is 2.
Hence, the y - intercept is [tex]b=2[/tex]
Equation of line:
The equation of line can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values, we get,
[tex]y=3x+2[/tex]
The equation of the line is [tex]y=3x+2[/tex]
Linear inequality:
The dotted line in the graph indicates that the inequality will be either < or >
Thus, the linear inequality will be [tex]y<3x+2[/tex] or [tex]y>3x+2[/tex]
From the graph, it is obvious that the shaded region does not contain the coordinates (0,0)
Hence, we need to determine the inequality that does not contain the coordinate (0,0)
Let us consider the inequality [tex]y<3x+2[/tex]
Substituting (0,0) in the inequality [tex]y<3x+2[/tex], we get;
[tex]0<3(0)+2[/tex]
[tex]0<2[/tex]
Since, the inequality satisfied the condition, it contains the coordinate (0,0)
Now, considering the inequality [tex]y>3x+2[/tex] and substituting (0,0), we have;
[tex]0>3(0)+2[/tex]
[tex]0>2[/tex]
Since, the inequality does not satisfy the condition, it does not contain the coordinate (0,0)
Thus, the linear inequality represented in the graph is [tex]y>3x+2[/tex]
Hence, Option B is the correct answer.