Writing Systems from Graphs
Writing systems of linear inequalities from graphs is a Grade 11 Algebra 1 skill from enVision Chapter 4 that reverses the graphing process. Each boundary line is identified by its equation from slope and y-intercept, then the inequality symbol is determined by whether the line is solid (<= or >=) or dashed (< or >) and which side is shaded. A solid line through (0, 2) and (1, 4) with shading below gives y <= 2x + 2. A dashed horizontal line at y = -1 with shading above gives y > -1. A solid vertical line at x = 3 with left-side shading gives x <= 3.
Key Concepts
To write a system of linear inequalities from a graph, identify each boundary line's equation using slope and y intercept, then determine the inequality symbol based on whether the line is solid ($\geq$ or $\leq$) or dashed ($ $ or $<$) and which side is shaded.
Common Questions
How do you write an inequality from a boundary line graph?
Find the line equation using slope and y-intercept. Determine the inequality symbol from the line type (solid = or =, dashed = strict) and the shaded side.
What does a solid boundary line indicate?
A solid line means the boundary is included in the solution, so the inequality uses <= or >=.
What does a dashed boundary line indicate?
A dashed line means the boundary is not included, so the inequality uses strict < or > symbols.
A solid line through (0,2) and (1,4) with shading below: what is the inequality?
Slope = (4-2)/(1-0) = 2, y-intercept = 2. Line is y = 2x + 2. Solid line + shading below means y <= 2x + 2.
How do you determine which side of the line is shaded?
Test a point not on the line in the original inequality. If it satisfies the inequality, that side is shaded; if not, shade the other side.
What inequality describes a vertical line x = 3 with shading to the left?
x <= 3. The solid line means equal or less than, and shading to the left means values smaller than 3.