Review

Last class topic was about how linear equations solutions can be thought as all points that creates a line. Whe have something like this:

or

And we can choose wathever value we like for one variable, and the other gets fixed and related. There is one $y$ value for each $x$ value, and vice-veresa, buth this pairs are unique.

Getting the line

If we plot linear equations solutions, we'll get lines. That's easy. But how can one identify which equation formed a given line?

Run and Rise

A way of telling which function (equation) belongs to a given plot it's to find $a$ and $b$. Fin $b$ it's straight because one has to look at $y$ axis interception. But ¿what about $a$?. A method is as follows:

1. Step on a point that belongs to the line (a solution, an $x$,$y$ pair)

2. Run to the right (left will be ok too, you'll se later) any given units you want (1,2,3)

3. Write down this value. We call it $\Delta x$

4. Rise (or go down) until you reach the line again

5. Count the units that took you there

6. Write down this value. We call it $\Delta y$

7. Do $\frac{\Delta y}{\Delta x}$

8. Result is $a$

Test what you've leanred