Answer: Last option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
The slope of a line can be found with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, knowing that this line goes through the points (0,3) and (2,-1), you get that its slope is:
[tex]m=\frac{-1-3}{2-0}\\\\m=-2[/tex]
By definition, a line intersects the y-axis when [tex]x=0[/tex].
Since the line goes through the point (0,3), you can identify that:
[tex]b=3[/tex]
Then, the equation of this line in Slope-Intercept form, is:
[tex]y=-2x+3[/tex]
You know that everything to the left of the dashed line is shaded, then the symbol of the inequality is [tex]<[/tex].
Therefore, the linear inequality that is represented by the graph is:
[tex]y<-2x+3[/tex]
