Recognize that a system of two equations in two variables can have no solution, one or more solutions, or infinitely many solutions.

• Recognize that a system of two equations in two variables can have no solution, one or more solutions, or infinitely many solutions
• Determine whether a graph is a function by using the vertical line test
• Determine the number of possible real roots by using a moveable horizontal line

• System of equations
• Root or zero of a function
• Intersection
• Vertical line test
• Infinitely many solutions
• Coinciding figures

Begin the lesson by manipulating a moveable line in the coordinate plane in relation to a fixed line. Discover what must be true for a system of linear equations to have one, infinitely many, or no solutions. Continue by manipulating a moveable line in the coordinate plane in relation to graphs of various fixed relations. Rotate the moveable line until it appears to be vertical on each page. Translate the line across the screen to determine if the graph is a function. Rotate the moveable line until it appears to be horizontal on each page. Translate the line up and down the screen to determine the possible number(s) of real roots of the graph. Given different systems, illustrate the possible number(s) of solutions.