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Question

solve y>3x-5 graphically. use your graph whether each of the following point is part of the solution. explain how to check :

(2,2) (-1,-9)(1,-2)(0,0)

Answer 1

Step 1:

The inequality is .

The points are , , and .

The graph of the inequality is the shaded region, where every point in the shaded region satisfies the inequality.

The graph of the equation   is the boundary of the region. Since the inequality symbol is >, the boundary is drawn as a dotted line to show that points on the line does not satisfy the inequality and the shaded region of the graph of   is the solutions to the inequality.

Step 2:

Graph:

Graph the inequality .

Shade the required region.

Plot all the points.

Note : The dashed line indicates that line does not satisfy the function.

Observe the graph:

The Points and are in the shaded region.

The Point touches the dashed line.

The Point  is not in the shaded region.

The solution of the inequality are and .

Comments

Step 3:

Check :

To check the solution, substitute the point in .

As the condition is not satisfied, is not  the solution of .

To check the solution, substitute the point in .

As the condition is not satisfied, is not  the solution of .

To check the solution, substitute the point in .

As the condition is satisfied, is the solution of .

To check the solution, substitute the point in .

As the condition is satisfied, is the solution of .

Solution :

The solution of the inequality are and .