Question

Graph each inequality. Determine which of the ordered pairs are part of the solution set for each inequality.$\mathit{y}\mathbf{\le }\mathbf{4}\mathbf{;}\mathbf{\{}\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{6}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{1}\mathbf{,}\mathbf{2}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{-}\mathbf{4}\mathbf{,}\mathbf{8}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{2}\mathbf{)}\mathbf{,}\mathbf{(}\mathbf{1}\mathbf{,}\mathbf{7}\mathbf{)}\mathbf{\}}$

Short answer

A graph of a given inequality is

The ordered pairs, and are part of the solution set.

As$(1,2)$and$(3,-2)$ are in the shaded half plane, they are part of the solution set.

Step-by-step solution

Step 1. Write steps to graph inequality.

1. If an inequality contains $<\text{or}>$, then use dotted line and if an inequality contains $\le \text{or}\ge$, then use solid line.

2. Use test point to determine which half plane should be shaded.

3. Shade the half plane that contains the solution.

Step 2. Select a test point.

Let $(0,0)$be a test point. Substitute 0 for $x$and 0 for $y$into $y\le 4$.

$(0,0)$

Therefore, the half plane containing the origin is the solution.

Step 3. Graph an inequality.

Graph an inequality, $y\le 4$and shade the half plane containing test point.

Step 4. Determine ordered pairs in solution set.

To determine which of the ordered pairs are part of the solution set, plot them on graph.

Plot $(3,6),(1,2),(-4,8),(3,-2)$and $(1,7)$.

As$(1,2)$and $(3,-2)$are in the shaded half plane, they are part of the solution set.