The equation of a 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.
In this case, you have the following inequality:
[tex]y\ge x-1[/tex]
Then, the equation of the line is:
[tex]y=x-1[/tex]
Where the values of "m" and "b" are:
[tex]\begin{gathered} m=1 \\ b=-1 \end{gathered}[/tex]
Since the sign of the inequality is:
[tex]\ge[/tex]
Then the line is solid and the shaded region is above the line.
Knowing the above, you can graph the inequality:
You can see that the line passes through the points (0,-1) and (3,2).
Therefore, the answer is: Option C.
