Question

Which graph represents the solution set to the system of inequalities?

Answer 1

Graph D (see attached).

Explanation:

Given system of inequalities:

`\begin{cases}y\leq (1)/(4)x-2\\\\y\geq -(5)/(4)x+2\end{cases}`

When graphing inequalities:

• Use a dashed line for < or >.
• Use a solid line for ≤ or ≥.
• Shade below the line for < or ≤.
• Shade above the line for > or ≥.

The graph of y ≤ (1/4)x - 2 is:

• A solid line with shading below the line.
• The slope of the line is positive (1/4).
• The y-intercept is (0, -2).

The graph of y ≥ -(5/4)x + 2 is:

• A solid line with shading above the line.
• The slope of the line is negative (-5/4).
• The y-intercept is (0, 2).

The graph that satisfies both these criteria is represented by option D.