The shaded region shown represents the solutions to which inequality? The dashed boundary line has equation .
For a graphed linear inequality, the boundary line shows where the two sides are equal, and the shading shows which points work. Read the shaded side to choose the inequality's direction, then check whether the line is dashed or solid to decide if equality counts. Keep the equation of the drawn line: changing its constant moves the boundary.
Hints
- Hint 1
A boundary line separates the shaded points from the unshaded ones. The shading is below the line. At the same -value, is a shaded point's -value less or greater than the line's -value?
- Hint 2
A dashed line leaves its own points out; a solid line includes them. Which symbol means less than, without allowing points whose -value equals the line's -value?
Step-by-step
Read the shading and the dashed line
Step 1Use the shading to choose a direction
No Desmos needed. The graph already shows the line and its shaded side. At any fixed , a shaded point is below the boundary line, so its -value is less than the line's -value, . Keep the : it's part of the given line, not something the shading changes.
- Step 2
Use the dashed line to exclude equality
The line is dashed, so points on it don't count. The symbol would include them; use the strict symbol instead. The shaded region represents . Choice A.