kinematics equations

Oh god oh god I almost forgot about this sdkfjlsdkjfs
God I've been so absent minded recently this isn't good at all.
This week, we were learning about the Big 5 equations of kinematics that we use to find the displacement, time, velocity, etc. I'll be explaining two of those that we can get from the graph.

The third equation we learned was displacement = V₁t + ½ at²
The fourth equation was displacement = V₂t - ½ at²

If we take a look at a velocity/time graph while trying to find the displacement, it might be confusing. We can add math into this and make it much simpler then it could be.

A normal velocity/time graph looks like this:

To find the displacement, we must find the area of the triangle created by the line, the dotted line, and a line not yet on the graph that will go horizontal from V1, since v = dt.
If we try to find the area by dividing the graph into a triangle and a rectangle, it would look like this:

To find the area of the triangle, you must use the equation a = 1/2bh. Since in here a=d, b=t and h= v2-v1, the equation will turn out:
d = 1/2 t(v2-v1)
And we learned that a = (v2-v1)/t, so v1 = at-v2
Therefore
d = 1/2t(v2-(at-v2))
d = 1/2t(v2-at+v2)
d = 1/2t(2v2-at)
d = v2t - 1/2at²
Which is the fourth equation. We can get the third equation by doing the exact same thing, except instead of isolating v1, we isolate v2.