Which linear inequality is represented by the graph?y ≤ x − 1y ≥ x − 1y < 3x − 1y > 3x − 1

First, work out the equation of the graph.
Equation of a straight line graph is given in the form [tex]y = mx+c[/tex] where [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the y-intercept.

The graph given shows the line intercept y-axis at (0, -1)

To work out the slope, choose any two coordinates then find their vertical and horizontal distance. Say we choose (0, -1) and (3, 0)
The vertical distance is 1 and the horizontal distance is 3, so the slope is
[tex]m = \frac{-1-0}{0-3}= \frac{-1}{-3}= \frac{1}{3} [/tex] 

Then form the equation for the line
[tex]y=mx+c[/tex]
[tex]y= \frac{1}{3}x-1 [/tex]→ Multiply each term by 3
[tex]3y = x - 3[/tex]

Now the inequality part, the shaded region is above the line, so the values intended are 'greater than' and the line is a bold line, so the inequality is 'greater than or equal to' and the symbol is ≥

The inequality is then
3y ≥ x - 3

Note: None of the options show this answer. Maybe check if the original options have been copied correctly.