The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0
<h3>How to Write a Linear Inequality?</h3>
To determine what sign to use, follow these rules:
- Use "<" or ">" when the boundary line is dotted or dashed.
- Use "<" or "≤" when the shaded area is under the boundary line (dotted or dashed).
- Use "≤" or "≥" when the boundary line is not dotted or dashed.
- Use ">" or "≥" when the shaded area is above the boundary line (dotted or dashed).
The graph given has the following features:
- It has a boundary line that is dotted/dashed.
- It has a shaded area that is under the boundary line.
- Thus, the inequality sign we would use is, "<".
Find the slope:
Slope (m)= rise/run = -(2 units) / (2 units).
Slope (m) = -1.
The y-intercept (b) = -2.
Substitute m = -1 and b = -2 into y < mx + b:
y < (-1)x + (-2)
y < -x - 2
Rewrite
x + y < -2
x + y + 2 < 0
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