Finding Inequalities from Regions

Interpreting Graphical Inequalitiesvideo

Interpreting graphical inequalities

How do I know which inequalities are shown on a graph of shaded regions?

• To identify the inequalities represented by the shaded regions on a graph:

  • Find the equation of each line on the graph

    • You may have to calculate the gradient and find the y-intercept to use $y=mx+c$

    • Vertical lines have the form $x=k$

    • Horizontal lines have the form $y=k$

  • Remember that lines are drawn using:

    • a solid line for ≤ or ≥, indicating a line included in the region

    • a dotted line for < or >, indicating a line not included in the region

  • Replace the = sign with the relevant inequality

    • ≤ or < if region is below line

    • ≥ or > if region is above line

    • (Use a point to test if not sure)

  • For vertical lines:

    • ≤ or < if region is to the left of the line

    • ≥ or > if region is to the right of the line

    • (Use a point to test if not sure)