Graph x+2y>=-9

Problem

x+2*y≥−9

Solution

1. Convert the inequality into an equation to find the boundary line by replacing the inequality sign with an equals sign.

x+2*y=−9

2. Find the intercepts to plot the boundary line. Set x=0 to find the yintercept and y=0 to find the xintercept.

0+2*y=−9⇒y=−4.5

x+2*(0)=−9⇒x=−9

3. Determine the line type based on the inequality symbol. Since the symbol is ≥ the boundary line is solid, indicating that points on the line are included in the solution set.

Boundary: *x+2*y=−9* (solid line)

4. Test a point not on the line, such as (0,0) to determine which side of the line to shade.

0+2*(0)≥−9

0≥−9

5. Shade the region that makes the inequality true. Since 0≥−9 is a true statement, shade the side of the line containing the origin (0,0)

Shade above the line *y=−0.5*x−4.5

Final Answer

x+2*y≥−9

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