criteria

1. solve problems using analytic geometry that involve lines, line segments, intersecting lines and, verify properties of geometric shapes such as triangles and quadrilaterals

2. use evidence and reasoning to explain strategies and support mathematical ideas.

Task:

Build as few linear systems (of two lines) as possible to satisfy each criteria at least once. You are to problem solve and complete the task using Desmos. You can discuss everything with your peers and seek clarification from your teacher but you must submit your own solution and explanation.

Your systems must meet all 6 of these criteria:

A. The solution is in the third quadrant B. One equation in the system is y = 2 C. The lines in the system have identical but oppositely-signed x-intercepts. D. Both lines in the system have negative slopes E. Both coordinates of the solution are rational numbers. F. The x-coordinate of the solution is triple that of the y-coordinate of the solution

Questions:

1. Which criteria (A to F) can be PAIRED together in one system? Explain.

2. Which criteria (A to F) cannot be PAIRED together in one system? Explain.

3. What is the least number of linear systems you are using to meet the 6 criteria? State the equations of all your systems, include Desmos screenshots of each system here and identify which system satisfies which criteria.

4. Describe the thought process you went through to make systems.