x+y≤6 graph the linear inequality on a plane

1 answer

To graph the inequality x + y ≤ 6, we need to graph the line x + y = 6 first and then shade the region below it.

First, let's graph the line x + y = 6 by finding the x and y-intercepts.

When x = 0, y = 6, giving us the point (0, 6).

When y = 0, x = 6, giving us the point (6, 0).

Plot these two points and draw a straight line through them.

Next, we need to shade the region below the line. Since the inequality is ≤ (less than or equal to), we will shade the region below the line.

The graph should look like this:

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The shaded region represents all the points that satisfy the inequality x + y ≤ 6.