The shaded region shown represents the solutions to which inequality? The dashed boundary line has equation .
For a graphed linear inequality, identify the boundary line, then use the shading to choose vs. , and use dashed (strict) vs. solid (inclusive) to choose between and (or and ).
Hints
Start with the boundary line
Use the given boundary equation as the dividing line between shaded and unshaded regions.
Use where the shading is
Decide whether shaded points have -values greater than or less than the boundary line’s -values.
Use dashed vs. solid
A dashed boundary means the line itself is not included in the solution set (strict inequality).
Desmos Guide
Graph the boundary line
In Desmos, enter to graph the boundary line.
Decide which side is shaded
Test a point clearly in the shaded region (for example, ). Compare its -value to the line’s -value at the same to determine whether the shaded region corresponds to being less than or greater than the line.
Use dashed vs. solid to choose the symbol
Because the boundary is dashed, use a strict inequality ( or ), not or . Combine this with the shading direction to get the correct inequality.
Step-by-step Explanation
Use shading and boundary type to choose the inequality
The boundary line is .
Because the region is shaded below the line, the solutions have less than .
Because the boundary is dashed, points on the line are not included, so the inequality is strict.
Therefore, the inequality is .