Use the graph to answer the question.

Question

Information
A graph.Short description, A graph.,Long description,
On a coordinate plane, there are two intersecting lines.

A solid line with a positive slope crosses the x-axis at (negative 2.5 comma 0) and the y-axis at (0 comma 5).
A dotted line with a negative slope crosses the y-axis at (0 comma 5) and the x-axis at (5 comma 0).
The lines intersect at (0 comma 5). The area below and between the two lines is shaded.

Question
Move symbols to the boxes to complete the system of inequalities represented by the graph.

Response area with 2 blank spaces
y

Blank space 1 empty

2 x plus 5

5

Blank space 2 empty

x plus y


Answer options with 5 options.

Answer 1

Based on the description of the graph and the lines, we can infer the following inequalities:

1. The line with a positive slope crosses the x-axis at \((-2.5, 0)\) and the y-axis at \((0, 5)\). The equation of this line can be written in slope-intercept form as \(y = 2x + 5\). The area above this line should not be included since it is below the line, leading to the inequality \(y \leq 2x + 5\).

2. The dotted line with a negative slope crosses the y-axis at \((0, 5)\) and the x-axis at \((5, 0)\). This gives it a slope of \(-1\) and can be described by the equation \(y = -x + 5\). Since the area below this line is shaded, the corresponding inequality is \(y \geq -x + 5\).

Therefore, the system of inequalities is:

1. \(y \leq 2x + 5\) (Blank space 1)
2. \(y \geq -x + 5\) (Blank space 2)

So the completed response area should read:

• Blank space 1: \(2x + 5\)
• Blank space 2: \(-x + 5\)

In short, to fill in the response area:

• Blank space 1: \(2x + 5\)
• Blank space 2: \(-x + 5\)

Thus, the answer options that include the components \(y\), \(2x + 5\), and \(-x + 5\) will allow you to form the inequalities representing the graph.