Concept: Linear Equations
We're not just drawing lines on paper. We're trying to learn something. We're trying to see and examine relationships between two things.
Current Problem:
Year vs. Median Income.
How has median income changed over the years? Let's plot a few points on a Cartesian coordinate system and see if there is a linear relationship.
Since we have been studying linear equations and their graphs, we can use all of our graphing skill and maybe learn something new.
We have: (1980,17000) and (2000,42000)
Okay, it looks like median income might be increasing over the years. How fast might it be increasing? Well, we have ($42000 - $17000)/(2000 yrs - 1980 yrs) = 25000/20 ($/yr) = $1250 / year.
Oh, I see. Maybe we can believe that Median Income increases $1250 per year. Can we create an equation so that we can see what the Median Income might have been on other years that we were not able to tabulate?
Again, we studied linear equations, so we know how to draw a graph if we can define a Cartesian Coordinate system and then gather enough information to define a unique line.
x-axis Years
y-axis Median Family Income
I see it now. We have a point (1980,17000) and we have a slope ($1250/yr). Let's use the Point=Slope form of a line and we will have our equation!
(y-k) = m(x-h)
The point we have is (h.k) = (1980 yrs,$17000). Let's substitute that.
(y - 17000) = m(x - 1980)
We calculated the slope in our previous discovery. Substitute that.
(y - 17000) = (1250)(x - 1980)
There is the line we need. Put that in a more useful form and you'll nearly be done.
Now how about it? Did the thought-process narrative do you any good?