Hi Amy... I'll add:
The slope is the x-coefficient, or x-multiplier. 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 x-y 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 y-offset 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 y-coordinate :-)