Graph: {(y > 1/2x-1),(y < -1/4x-2)

Question

Graph: {(y > 1/2x-1),(y < -1/4x-2)

Answer 1

Graph each one as if the weren't inequalities. That'll give you two lines. Then, for each line, test a point, for example the origin, to see if it satisfies the original inequality. If the point satisfies the inequality, shade the region containing your test point, otherwise, shade the region on the other side of the line. The answer will be the region that satisfies both inequalities. For this problem, make sure you draw your lines as dashed lines. You would use solid lines if your inequalities were also 'equal to' rather than solely greater than or less than.

Answer 2

To graph linear inequalities, begin by graphing the similar line.  For example, for the inequality y > 1/2x - 1, graph the line y = 1/2x - 1.

Since the inequality is greater than, not greater than or equal to, you will want to make the line dashed rather than solid (if you already drew a solid line, just erase pieces to turn it into a dashed line.

Once the (dashed) line is drawn, choose a point that is not on the line.  For example, the point (0,0) is not on the line y = 1/2x - 1.  Substitute the point into the original inequality.

0 > 1/2*0 - 1

0 > 0 - 1

0 > -1

The statement is true, so (0,0) is an acceptable solution for the inequality.  If a point satisfies the inequality, then all points on that side of the line satisfies the inequality.  If the point did not work, then all points on the other side of the line satisfy the inequality.  Draw lines (either vertical or horizontal) on the correct side of your line.  These will represent the portion of the graph that satisfied the inequality.

Repeat the above procedure for the second inequality, but have your "shading" lines run perpendicular to those from the first equation.

The graph should be divided into four sections by the two lines.  One section should have both horizontal and vertical lines running through it.  Shade this section.  This shaded section is the set of solutions for the system of linear inequalities.