Hi Amy... I'll add:
The slope is the xcoefficient, or xmultiplier. From our sample problem, we know we have one term, 4x
We also know that when we have a set of points from a graph, then we have an xy coordinate (location) that gives us both x and y at the same time (same place on the equation graph), and both can be plugged into the equation.
Coordinates are usually given as (x, y), and from our sample we have x = 1, and y = 3. Now we can just plug these into the standard
y = mx + b format for a linear (straight line) equation: 1 = 4(2) + b.
"b" is the value y has when x = 0; you can think of it as a yoffset above or below zero, because if b = 0, then when x = 0, y would also = 0, and our line would pass through (0, 0).
(y = m(0) + 0; y = 0). We can find b by solving y=mx+b for b: b = y  mx.
In our sample, b = (1)  (4)(3); b = 1 + 12, so b = +11. Our final equation: y = 4x + 11
To prove it: y = 4(3) + 11; y = 12 + 11 = 1, which is the original ycoordinate :)
1/14/2013

Bill F.