Question

1. When graphing the boundary line, what indicates the graphing of a solid line? 2. When graphing the boundary line, what indicates the graphing of a dashed line? 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

Part 1:

When graphing the boundary line of a linear inequality, the line is solid when the inequality is not strictly greater/less than.

i.e. when ≤ or ≥ is used.



Part 2:

When graphing the boundary line of a linear inequality, the line is dashed when the inequality is strictly greater/less than.

i.e. when < or > is used.



Part 3:

When using the slope-intercept form to graph linear inequalities, the side above the line is shaded when the linear inequality uses the greater than (>) sign and the side below the line is shaded when the linear inequality uses the less than (<) sign.



Part 4:

An alternative method that can be use to indicate that the appropriate regions are shaded correctly is to select an arbitrary point above and below the line and see which one satisfies the given inequality.



Part 5:

When graphing the shaded regions for a system of linear inequalities, the solution set of the system is indicated by where the shaded reqions of the system of linear inequalities coincides.