Problem 90 - Algebra and Trigonometry

Question

What does a solid line mean in the graph of an inequality?

Step-by-Step Solution

Answer

In the graph of an inequality, a solid line symbolizes that all points on the line are included in the solution to the inequality. It usually represents the 'equal to' component of the inequality.

Step 1: Understanding Lines in Graphs

If you graph an inequality on the coordinate plane, use a solid or dashed line to represent the boundary of the inequality. This boundary separates the plane into two regions. One of these regions will represent values that make the inequality true, while the other does not.

Step 2: Definition of Solid Line

A solid line on a graph of an inequality represents an 'equal to' part of the inequality. Whenever the relation within the inequality includes '=,' a solid line signifies that any point on that line is a solution to the inequality.

Step 3: Working with Solid Lines

When working with solid lines, you can pick a point on the line, plug its coordinates into the equation of the inequality. If it makes the inequality true, you'll know that every point on the line is a solution to the inequality.