Analyzing Graphs that Represent Linear Equations and Inequalities

2.15.1 Analyzing Graphs that Represent Linear Equations and Inequalities

2.15.1 • Analyzing Graphs that Represent Linear Equations and Inequalities

Warm Up

Compare each of the following graphs, then list a reason for each graph why it would not belong with the other three.

Graph A.

Graph of two lines on a coordinate plane

Graph B.

Graph of two inequalities on a coordinate plane

Graph C.

Graph of two inequalities on a coordinate plane

Graph D.

Graph of an inequality on a coordinate plane
This table displays four mathematical graphs, featuring lines and inequalities plotted on a coordinate plane, for visual reference.

Compare your answer:

Your answers may vary,, but here are some samples.

  • Graph A is the only set of graphs that represents a system of equations. It is the only system with exactly one solution.
  • Graph B is the only set of graphs that represents a system of inequalities with no solutions.
  • Graph C is the only set of graphs in which the boundaries are horizontal and vertical lines. It is the only one representing a system with an infinite number of solutions.
  • Graph D is the only graph that does not represent a system. It only represents one inequality.