graph the linear inequality on a plane x+y≤4

Answer 1

To graph the linear inequality x + y ≤ 4, we can start by graphing the corresponding equation x + y = 4.

First, let's create a table of values for this equation:

x | y
------
0 | 4
4 | 0
1 | 3

Plotting these points on a coordinate plane, we can connect them to form the line x + y = 4. This line goes through the points (0, 4), (4, 0), and (1, 3).

Next, we need to determine which region of the plane satisfies the inequality x + y ≤ 4. To do this, we need to determine if the inequality is true or false when substituting test points.

For example, let's test the point (0, 0) in the inequality.
0 + 0 ≤ 4
0 ≤ 4
This is true, so the point (0, 0) satisfies the inequality.

Choosing test points within the regions defined by the line, we can shade the region that satisfies the inequality. In this case, we shade the region below the line to represent x + y ≤ 4.

The graph would look like this:

y
|
| x+y≤4
| /\
|/__\________
0 4 x