What do you notice about each solution? : Picture 1 - They never intersect/touch. Picture 2 - They are intersecting. Picture 3 - They are on top of each other.
What do you notice about the graphs for each set of equations? : Picture 1 - The lines are parallel. Picture 2 - They are intersecting. Picture 3 - They are on top of each other. (otherwise known as coincident lines).
What do you notice about each set of equations? : Picture 1 - They have the same slope but different y-intercepts. Picture 2 - Both the slopes and y-intercepts are different for each equation. Picture 3 - They have the same slope and same y-intercept.
What generalization can you make? : Picture 1 - When equations have the same slope but different y-intercepts they will be parallel when graphed. Picture 2 - When the equations have different slopes and different y-intercepts they will be intersecting. Picture 3 - When the equations are the same they will be coincident lines when graphed.
