Question

activity 2: sketching solutions to inequalities
here is a graph that represents solutions to the equation ( x - y = 5
ightarrow )
sketch 4 graphs representing the solutions to each of these inequalities:
( x - y lt 5 ) dashed line
( x - y gt 5 ) dashed line
( x - y leq 5 ) solid line
( x - y geq 5 ) solid line

Explanation:

Step1: Understand the inequality type

For inequalities \(x - y>5\) and \(x - y < 5\), the boundary line \(x - y=5\) (or \(y=x - 5\)) is not included in the solution set. So, we use a dashed line.

Step2: Analyze non - strict inequalities

For inequalities \(x - y\geq5\) and \(x - y\leq5\), the boundary line \(x - y = 5\) (or \(y=x - 5\)) is included in the solution set. So, we use a solid line.

Answer:

The first cell (\(x - y>5\)) has a dashed line because the inequality is strict (\(>\)). The second cell (\(x - y < 5\)) has a dashed line because the inequality is strict (\(<\)). The third cell (\(x - y\geq5\)) has a solid line because the inequality is non - strict (\(\geq\)). The fourth cell (\(x - y\leq5\)) has a solid line because the inequality is non - strict (\(\leq\)).