This document discusses how to represent linear inequalities graphically. Less than (<) and greater than (>) symbols are shown with dashed lines, while less than or equal to (≤) and greater than or equal to (≥) symbols are shown with solid lines. For inequalities in x, a vertical line is drawn at the x-value, with dotted lines for strict inequalities and solid lines for non-strict inequalities. For inequalities in y, a horizontal line is drawn at the y-value, also using dotted lines for strict inequalities and solid lines for non-strict inequalities. Shading is used to indicate the side of the line included in the solution set.

1. LINEAR INEQUALITIES
SOLUTION ON A GRAPH

2. FOR INEQUALITIES ON THE
COORDINATE PLANE
< 𝑎𝑛𝑑 > are represented with a dashed
line.
≤ 𝑎𝑛𝑑 ≥ are represented with a solid
line.

3. INEQUALITIES IN 𝒙 only
Inequalities with the variable ′𝒙′ produce a
vertical line on the graph.
We find the value on the x-axis and draw a
DOTTED LINE if the inequality is strictly less
than or greater than.
If the inequality is > 𝒐𝒓 ≥, shade the right
side of the line.

4. INEQUALITIES IN 𝒙 only
Inequalities with the variable ′𝒙′ produce a
vertical line on the graph.
We find the value on the x-axis and draw a
SOLID LINE if the inequality is less than or
equal to ≤ or if the inequality is greater
than or equal to (≥).
If the inequality is < 𝒐𝒓 ≤, shade the left
side of the line.

5. INEQUALITIES IN 𝒚 only
Inequalities with the variable 'y' produce a
horizontal line on the graph.
We find the value on the y-axis and draw a
DOTTED LINE if the inequality is strictly less
than or greater than.
If the inequality is > 𝒐𝒓 ≥, shade above the
line.

6. INEQUALITIES IN 𝒚 only
Inequalities with the variable 'y' produce a
horizontal line on the graph.
We find the value on the y-axis and draw a
SOLID LINE if the inequality is less than or
equal to (≤) or if the inequality is greater
than or equal to (≥).
If the inequality is < 𝒐𝒓 ≤, shade below the
line.

7. THE END.