solve and graph

Question

x + y is less than or equal to 8 how would i solve and graph this.

Answer 1

  

The graph of the inequality x + y ≤ 8 is the shaded region and boundary of the inequality is x + y = 8.

y ≤ -x + 8

1. Draw the coordianate plane.

2.  Since inequality x + y ≤ 8 symbol is ≤, the boundary is included in the solution set. Graph the boundary of the inequality x + y = 8 with solid line.

3.  To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).

Substitute and x = 0 and y = 0 in original inequality x + y ≤ 8.

0 + 0 ≤ 8

0 ≤ 8

The statement is true.

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