I don't understand how to graph linear inequalities in two variables

Question

The equation they want us to graph is y< 2x + 3. but when they show the graph they show it graphed as -2x + 3 and I am not sure how they changed the 2x to a -2x.

Answer 1

Given inequality is y < 2x+3

The graph of the inequlity y < 2x+3 is the shaded region and boundary of the inequality is y = 2x+3

Draw a coordinate plane.

Since inequality symbol is <, the boundary is not included in the solution set.

Graph the boundary of the  inequality y = 2x+3 with red colour dashed line.

To determine which half plane to be shaded use a test point in either half plane.

A simple choice is (0,0) substitute x = 0, and y = 0 in original inequality y < 2x+3

0 < 3

The statement is true.shade the region that contains a point (0,0)

when it is changed y < -2x+3

To determine which half plane to be shaded use a test point in either half plane.

A simple choice is (0,0) substitute x = 0, and y = 0 in original inequality y < -2x+3

0 < 3

the statement is true. shade the region that  contains point (0,0)

Graph the boundary of the  inequality y < -2x+3 with fuchsia colour dashed line.

Graph