The inequality represented by the graph is y ≤ x + 3.
The graph shows a straight line passing through (-3,0) and (0,-3).
To determine the inequality represented by the line, we need to find the slope and y-intercept.
The slope of the line can be calculated by using the formula: m = (change in y)/(change in x).
Substituting the coordinates, we get: m = (-3 - 0)/(0 - (-3)) = -3/-3 = 1.
The y-intercept can be determined by substituting the coordinates of one of the points into the equation y = mx + b and solving for b.
Using the point (-3,0), we have: 0 = 1*(-3) + b, which gives b = 3.
So, the equation of the line is y = x + 3.
Since the line passes through the points on or below it, the correct inequality is y ≤ x + 3 (Option A).
The probable question may be:
Which inequality does this graph show?
line is passing through (-3,0) to (0,-3)
A. y≤-x-3
B. y≥-x+3
C. y≥x-3
D. y≥x+3