Hi, there are multiple ways you can set this up to solve algebraically. Here's how I would do it:
Note that lines are of the form y = mx + b. Remember that m is rise over run, so
m = (y2 - y1)/(x2 - x1) = (600-650)/(8-6) = -50/2 = -25
and we want "b" so that: y(6) = 650 or 6m + b = 650
(we know m = - 25).
6(-25) + b = 650,
-150 + b = 650
b = 650 + 150 = 800
To solve this using linear algebra, you can set up a matrix! (This was posted in Linear Algebra, if unnecessary feel free to use above solution)
We have:
6m + b = 650 & 8m + b = 600 by plugging in the points into the equation y = mx + b.
As a matrix-vector equation, this is ( 6 1 / 8 1 | 650 600 ) [Sorry, Wyzant doesn't allow for Matrices].
Simply row reduce with gaussian elimination and you have m & b!
Hope this helps.
