Graph using linear inequality

x - y less than or equal to 1

To graph the linear inequality "x - y ≤ 1", we will follow these steps:

Step 1: Start by graphing the equation of the line x - y = 1.
Step 2: Choose a point not on the line to determine which side of the line to shade.
Step 3: Shade the region that includes the chosen point.

Let's begin:

Step 1: Graph the equation x - y = 1:
To do this, we can rewrite the equation in slope-intercept form: y = x - 1.
This equation represents a line with a slope of 1 and a y-intercept of -1. We can obtain additional points by choosing values for x.

Here is a table of values for x and their corresponding y-values:
x | y
-2 | -3
0 | -1
2 | 1

Plotting these points on a graph and connecting them with a straight line will give us the graph of the equation x - y = 1.

Step 2: Choose a point not on the line:
We can choose the origin (0,0) as a test point to determine which side to shade.

Step 3: Shade the region that includes the chosen point:
To determine which side of the line to shade, substitute the test point (0,0) into the original inequality x - y ≤ 1.

0 - 0 ≤ 1
0 ≤ 1

Since the inequality is true, we know that the shaded region should be below the line x - y = 1.

Now, plot a dashed line to represent the equation x - y = 1 and shade the region below the line.

In summary, the graph of the linear inequality x - y ≤ 1 is a dashed line with a shading below the line.