Question

please print test, show all necessary work and circle all answe

1. graph the inequality

( y leq 2x - 5 )

Explanation:

Step1: Analyze the boundary line

The inequality is \( y \leq 2x - 5 \). First, consider the boundary line \( y = 2x - 5 \). This is a linear equation in slope - intercept form \( y=mx + b \), where the slope \( m = 2 \) and the y - intercept \( b=- 5 \). Since the inequality is \( \leq \), the boundary line should be a solid line (because the points on the line are included in the solution set).

Step2: Find two points on the boundary line

To graph the line \( y = 2x-5 \), we can find two points:

• When \( x = 0 \), \( y=2(0)-5=-5 \). So one point is \( (0,-5) \).
• When \( x = 3 \), \( y=2(3)-5 = 6 - 5=1 \). So another point is \( (3,1) \). Plot these two points and draw a solid line through them.

Step3: Determine the region to shade

To determine which side of the line to shade, we can use a test point that is not on the line. A common test point is \( (0,0) \). Substitute \( x = 0 \) and \( y = 0 \) into the inequality \( y\leq2x - 5 \):
\( 0\leq2(0)-5\)
\( 0\leq - 5 \), which is false. So the point \( (0,0) \) is not in the solution set. We shade the region that does not contain \( (0,0) \), which is the region below the line \( y = 2x-5 \).

(Note: Since this is a graphing problem, the final answer is the graph with a solid line \( y = 2x - 5 \) and the region below the line shaded. If we were to describe the key steps for the graph, the above steps are the necessary work. If we were to present the graph, we would have a coordinate plane with the solid line passing through \( (0,-5) \) and \( (3,1) \) and the area below the line shaded.)

Answer:

The graph has a solid line \( y = 2x - 5 \) (passing through \((0, - 5)\) and \((3,1)\)) with the region below the line shaded.