Question

step 1 of 3: graph the solution set of the first linear inequality. {x > - 7, y ≥ - 4} choose the type of boundary line: solid (—) dashed (---) enter two points on the boundary line: ( , )( , ) select the region you wish to be shaded: a b answer 5 points the line will be drawn once all required data is provided and will update whenever a value is updated. the regions will be added once the line is drawn. enable zoom/pan keypad keyboard shortcuts

Explanation:

Step1: Analyze the inequalities

We have \(x > - 7\) and \(y\geq - 4\). The inequality \(x > - 7\) has a vertical boundary line \(x=-7\) and the inequality \(y\geq - 4\) has a horizontal - boundary line \(y = - 4\).

Step2: Determine the boundary - line types

For \(x > - 7\), since the inequality is strict (\(>\)), the boundary line \(x=-7\) is dashed. For \(y\geq - 4\), since the inequality is non - strict (\(\geq\)), the boundary line \(y = - 4\) is solid.

Step3: Find points on the boundary lines

For the line \(y=-4\), two points on it can be \((0, - 4)\) and \((5,-4)\).
For the line \(x=-7\), two points on it can be \((-7,0)\) and \((-7,5)\).

Step4: Determine the shaded region

For \(x > - 7\), we shade to the right of the line \(x=-7\). For \(y\geq - 4\), we shade above the line \(y = - 4\). The intersection of these two regions is the region we want to shade.

For the boundary - line type:
The line \(x=-7\) is Dashed and the line \(y = - 4\) is Solid.
Two points on \(y=-4\) can be \((0,-4)\) and \((5,-4)\) (answers may vary).
The region to be shaded is the region to the right of \(x = - 7\) and above \(y=-4\).

Answer:

Type of boundary line for \(x > - 7\): Dashed
Type of boundary line for \(y\geq - 4\): Solid
Two points on \(y=-4\): \((0,-4)\), \((5,-4)\)
Region to be shaded: The region to the right of \(x=-7\) and above \(y = - 4\)