The inequality x < y="" can="" be="" represented="" graphically="" on="" a="" coordinate="" plane.="" here's="" />

Plotting the Line x = y
To graph this inequality, we first need to plot the line x = y. This is the line where the x and y coordinates are equal. To plot this line, we simply draw a diagonal line from the origin (0, 0) to the point (1, 1).

Shading the Region Below the Line
Since we want to graph the inequality x < y,="" we="" need="" to="" shade="" the="" region="" that="" satisfies="" this="" inequality.="" in="" other="" words,="" we="" need="" to="" shade="" the="" region="" below="" the="" line="" x="y." this="" includes="" all="" points="" where="" the="" x-coordinate="" is="" less="" than="" the="" y-coordinate.="" />

Final Graph
The final graph should show the line x = y and a shaded region below this line. The shaded region should extend infinitely in all directions.

Interpreting the Graph
The graph shows all possible solutions to the inequality x < y.="" any="" point="" in="" the="" shaded="" region="" satisfies="" this="" inequality,="" while="" any="" point="" outside="" the="" shaded="" region="" does="" not.="" for="" example,="" the="" point="" (2,="" 3)="" satisfies="" the="" inequality="" since="" 2="" is="" less="" than="" 3,="" but="" the="" point="" (3,="" 2)="" does="" not="" since="" 3="" is="" not="" less="" than="" 2.="" y.="" any="" point="" in="" the="" shaded="" region="" satisfies="" this="" inequality,="" while="" any="" point="" outside="" the="" shaded="" region="" does="" not.="" for="" example,="" the="" point="" (2,="" 3)="" satisfies="" the="" inequality="" since="" 2="" is="" less="" than="" 3,="" but="" the="" point="" (3,="" 2)="" does="" not="" since="" 3="" is="" not="" less="" than="" />