Question

3. When using the slope-intercept form to graph linear inequalities, how do you know which side of the line to shade on?

4. What is an alternative method that can be use to indicate that the appropriate regions are shaded correctly? Be sure to explain how you would know this method indicates the shading is correct or incorrect.

5. When graphing the shaded regions for a system of linear inequalities, what indicates the solution set of the system?

Answer 1

3)

When we use slope intercept form(y=mx+b), when there is greater than sign (>) we will shade above the line and when it is small than sign (<) we will shade below the line.

For example y>2x +3, here we will shade above the line y=2x+3

4)

We will take a test point and check in the given inequality to find if it holds true. if it is true then we will shade the region containing the test point, otherwise if not holds true the region which does not contain the test point.

For example, y>x +2

we will first sketch the line y=x +2, which divides the plane in two parts. Now we take a test point say (0,0), plug in to y>x +2

0>0+2

0>2

Since this is false, we will shade the half region which does not contain the origin (0,0).

5)

The solution set of the system is the region in which if we pick any point, it will holds true in all the system of linear inequalities.