in y = mx + b, m is the slope, b is the y-intercept.

that is pretty much it. other than that, you need to know what slope and y-intercept means. the y-intercept is the number it cuts the y-axis at, that is, at the point (0,b). the slope is a measure of the rate of change of the line. it is how high you rise over how far you go, rise/run

example, if m = 3/2 it means if you are at one point on the line, then you can move 3 units up and 2 units to the right to get to another point.

when the slope is negative, you change one of those directions. for instance, if m = -3/2, then you would go 3 units up and 2 unitsto the left.

as far graphing goes. you only need two points to graph a given line. the y-intercept is given, so we only need to find one other point. the x-intercept is a nice one to find usually. then you can draw a straight line through both points to get your line

by the way, b doesn't shift anything along the x-axis. the formula for a function, lone constants affect the y-value, that is, they cause vertical shifts