Solution of Two Linear Equations- Open Middle Problem

Using the Integers 0-9 (without duplication), provide four sets of points that represent two distinct lines.  These lines can be written as two linear equations.  Then provide a fifth point that represents the intersection (or solution) of those equations.


Line 1: (__, __) and (__, __)

Line 2: (__, __) and (__, __)

Solution (__, __)

Write the equation of both lines.


One Solution, No Solutions, Infinite Solutions- Open Middle Problem

Using Integers (without repeating any number),  fill in the boxes to create the following types of Linear Equations:

Linear Equation with one solution:


Linear Equation with no solutions:


Linear Equation with infinite solutions:


What is the smallest Integer interval that could produce all three equations?

Linear Equation from 2 Points P2- Open Middle Problem

Using the numbers 1 to 4, using each only once, create 2 points that lie on a line with the following conditions:


1) The line has a positive y-intercept

3) The line has a negative y-intercept

3) The line has the greatest slope possible

4) The line has the smallest positive slope possible

5) The line has the greatest negative slope possible

6) The line has the smallest negative slope possible

Slope Point Form