Question

How can I graph the an inequality of 2x - 3y < 6.

Answer 1

Now inequality 2x - 3y  < 6.

2x - 3y  = 6

Subtract 2x  from each side.

-3y  = -2x + 6

Divide each side by negative 3.

y  = 2x / 3 - 2

1) Graph the line y  = 2x / 3 - 2.

2) Since the inequality symbol is < the boundary is not included the solution set.

Graph the boundary of the inequality 2x - 3y  < 6 with dotted line in blue colour.

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

A simple chioce is (0,0). Substitute x  = 0 and y  = 0 in original inequality.

2(0) - 3(0) < 6

0 < 6

The above statement is true.

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

Shaded in fuchsia colour.

Graph :