Question

Find a linear inequality with the following solution set. Each grid line represents one unit.

Answer 1

The linear inequality in standard form is: x + y < -2 or x + y + 2 < 0

How to Write a Linear Inequality?

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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