Given:
The given inequality is [tex]y \geq-x-3[/tex]
We need to determine the graph of the linear inequality.
Slope:
From the given inequality, the slope of the line is given by
[tex]m=-1[/tex]
Thus, the slope of the inequality is -1.
x and y intercept:
The x - intercept can be determined by substituting y = 0 in the equation.
Thus, we have;
[tex]0=-x-3[/tex]
[tex]x=-3[/tex]
Thus the coordinates of the x - intercept is (-3,0)
The y - intercept can be determined by substituting x = 0 in the equation.
Thus, we have;
[tex]y =-0-3[/tex]
[tex]y=-3[/tex]
Thus, the coordinate of the y - intercept is (0,-3)
Graphing the inequality:
Let us substitute the coordinate (0,0) to determine the shaded portion.
Thus, we get;
[tex]0\geq -0-3[/tex]
[tex]0\geq -3[/tex]
Thus, the coordinate satisfies the inequality.
Hence, the everything to the right of the line is shaded.
Also, the symbol "≥" denotes the solid line.
Thus, On a coordinate plane, a solid straight line has a negative slope and goes through (negative 3, 0) and (0, negative 3). Everything to the right of the line is shaded.
Hence Option A is the correct answer.
