Option B: [tex]y> 3x + 2[/tex] is the linear inequality represented in the graph.
Explanation:
From the graph, the coordinates are [tex](0,2)[/tex] and [tex](-3,-7)[/tex]
First, we shall find the equation of the line.
The equation of the line can be determined using the formula,
[tex]y=mx+b[/tex]
The slope of the two points is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the coordinates, we have,
[tex]m=\frac{-7-2}{-3-0}[/tex]
[tex]m=\frac{-9}{-3}[/tex]
[tex]m=3[/tex]
The slope is [tex]m=3[/tex]
The y -intercept is the value of y when x is equal to zero.
Hence, from the coordinates, the y - intercept is [tex]b=2[/tex]
Substituting the slope [tex]m=3[/tex] and the y- intercept [tex]b=2[/tex] in the formula [tex]y=mx+b[/tex], we get,
[tex]y=3x+2[/tex]
Thus, the equation of the line is [tex]y=3x+2[/tex]
From the graph, it is obvious that the line is dotted and the upper region of the line is shaded.
This means that the value of y is greater.
Hence, the equation of the inequality is [tex]y> 3x + 2[/tex]
Therefore, Option B is the correct answer.
