GRAPH A LINEAR INEQUALITY IN THE COORDINATE PLANE

Example 1 :

Sketch the graph of the following linear inequality.

y ≤ (3x/5) - 5

Solution :

Step 1 :

Consider the given inequality as equation.

y  =  (3x/5) - 5

The equation above is in slope-intercept form.

Slope  =  3/5

y-intercept  =  -5 

Using the slope and y-intercept, sketch the graph of the line. 

Step 2 :

Take a point on either sides of the line and check which point satisfies the given inequality. 

Step 3 :

From the above step, the point (5, -5) satisfies the inequality. 

So, we have to shade the region from where the point (5, -5) is taken. 

Example 2 :

Sketch the graph of the following linear inequality.

y > -x - 5

Solution :

As we have done in example 1, we can do steps 1, 2 and 3 and get the graph of the inequality as shown below. 

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