Given:
Given that the graph of the inequality.
We need to determine the equation of the inequality.
Slope:
Let us substitute the coordinates (3,-1) and (-3,-3) in the slope formula, we get;
[tex]m=\frac{-3+1}{-3-3}[/tex]
[tex]m=\frac{-2}{-6}[/tex]
[tex]m=\frac{1}{3}[/tex]
Thus, the slope of the inequality is [tex]m=\frac{1}{3}[/tex]
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y-y_1=m(x-x_1)[/tex]
Substituting the point (3,-1) and the slope [tex]m=\frac{1}{3}[/tex], we get;
[tex]y+1=\frac{1}{3}(x-3)[/tex]
[tex]y+1=\frac{1}{3}x-1[/tex]
[tex]y=\frac{1}{3}x-2[/tex]
Thus, the equation of the line is [tex]y=\frac{1}{3}x-2[/tex]
Equation of the inequality:
From the graph, it is obvious that the line of the graph is a dashed line then inequality is either < or >
Thus, the inequality of the equation must be either [tex]y<\frac{1}{3}x-2[/tex] or [tex]y>\frac{1}{3}x-2[/tex]
Since, the shaded portion of the graph contains the point (0,0), we need to determine the inequality that contains the point.
Hence, substituting (0,0) in the inequality [tex]y<\frac{1}{3}x-2[/tex], we get;
[tex]0<\frac{1}{3}(0)-2[/tex]
[tex]0<2[/tex]
Thus, the coordinate (0,0) satisfies the condition, then the inequality of the given graph is [tex]y<\frac{1}{3}x-2[/tex]
Hence, the inequality of the graph is [tex]y<\frac{1}{3}x-2[/tex]
