Question

25 points! Help Please...

If you don't see the images, give it a second then.
DON'T answer saying you don't see the images, apologizing you could not help me, or give me a random "answer".
[I am sorry, I feel the need to say this for my questions (especially with the big-points ones), I have been answered with the incorrect responses so many times before.]

Thank you in advance.

Answer 1

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.