Answer:
[tex]y>3x+2[/tex] is represented in the graph.
Step-by-step explanation:
To find the linear inequality for the shown graph.
Steps:
Finding the equation of dotted line shown in the graph.
Equation of line is given by
[tex]y=mx+b[/tex]
where [tex]m[/tex] is slope of line and [tex]b[/tex] is y-intercept.
Given points: [tex](0,2) \ and\ (-3,-7)[/tex]
Slope of the line [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-7-2}{-3-0}[/tex]
[tex]m=\frac{-9}{-3}[/tex]
∴ [tex]m=3[/tex]
From the given points we can see that point of y-intercept is given i.e. the point where the line intersects the y-axis [tex](0,2)[/tex]
∴ [tex]b=2[/tex]
So equation of line:
[tex]y=3x+2[/tex]
Since the shaded area in the graph is above the line and the line is dotted this means that [tex]y[/tex] is greater than the equation of line.
So, the inequality can be given as:
[tex]y>3x+2[/tex]