Question

graph this inequality:

$y < 3$

plot points on the boundary line. select the line to switch between solid and dotted. select a region to shade it.

Explanation:

Step1: Identify the boundary line

The inequality is \( y < 3 \). The boundary line is \( y = 3 \), which is a horizontal line parallel to the x - axis passing through \( (x,3) \) for all \( x \). Since the inequality is strict (\( < \), not \( \leq \)), the boundary line should be a dotted line.

Step2: Determine the region to shade

To determine which side of the line \( y = 3 \) to shade, we can test a point not on the line. Let's choose the point \( (0,0) \). Substitute \( x = 0 \) and \( y=0 \) into the inequality \( y < 3 \). We get \( 0<3 \), which is true. So we shade the region below the line \( y = 3 \) (the region containing the point \( (0,0) \)).

Step3: Plot the boundary line

We can plot some points on the line \( y = 3 \). For example, when \( x = - 2 \), \( y=3 \) (point \( (-2,3) \)); when \( x = 0 \), \( y = 3 \) (point \( (0,3) \)); when \( x=4 \), \( y = 3 \) (point \( (4,3) \)). Since the inequality is strict, we draw a dotted line through these points. Then we shade the region below the dotted line \( y = 3 \).

(Note: Since this is a graphing problem, the final answer is the graph with a dotted line \( y = 3 \) and the region below the line shaded. But in text - based form, we describe the steps to graph it as above.)

Answer:

1. Draw a dotted horizontal line \( y = 3 \) (passing through points like \((-2,3)\), \((0,3)\), \((4,3)\) etc.).
2. Shade the region below the line \( y = 3 \) (the region where \( y\) - values are less than 3).