Find a solution to the linear inequality. y ≥ 4x - 5

Solution:

The solution to the linear inequality y ≥ 4x - 5 is determined with help of the graph which is shown below:

The line plotted in the above graph is y = 4x - 5.

The inequality y ≥ 4x - 5 is determined by taking a point on either side of the graph and testing the inequality.

Let us take a point above the line say (2, 15).

Substituting the value of x we get y = 4(2) - 5 = 3.

Now y coordinate 15 is greater than 3.

Therefore we see that the inequality is satisfied above the line y = 4x - 5.

The line y = 4x - 5 is also included in the inequality.

Let us take a point below the graph (4, 5).

Substituting the value of x = 4 in the equation we get y = 4(4) - 5 = 11 which is not greater than y = 5

Hence the inequality is not represented by the area above the line y = 4x - 5.

Find a solution to the linear inequality. y ≥ 4x - 5

Summary:

The solution to the linear inequality y ≥ 4x - 5 is the area above the line y = 4x - 5.