Chapter 3, Problem 8QC

To determine

To graph: The linear inequality $y<3$ .

Explanation of Solution

Given information:

The inequality $y<3$ .

Graph:

Consider the inequality $y<3$ .

The boundary of the inequality is the graph of the equation $y=3$ .

The equation $y=3$ is a horizontal line 3 units above the origin.

The inequality contains the sign of $<$ , so the boundary will be dashed.

Now, choose a point that does not lie on boundary say $\left(0,0\right)$ .

Substitute x as 0 and y as 0 in the equality $y<3$ .

  $0<3$

The above inequality is true so the shaded region will be towards the point $\left(0,0\right)$ .

The graph obtained is provided below,

  

Interpretation:

The graph of the inequality $y<3$ contain all the points whose y -coordinate is strictly less than 3.

To verify the region select any point from it say $\left(1,-1\right)$ . Substitute the value in the inequality,

  $-1<3$

The above inequality is true. So the region shaded represents the inequality $y<3$ .