Mr. Murray's Physics
Back to One Dimensional Motion Teacher Notes
Solving Linear Equations
When you have a blank graph, you have infinite number of points available. Any x-value could match up with any y-value. But when you have a line (whether experimentally found or given [theoretical]) you have restricted your universe to only those points that are on the graph. For any x you could find its y because you know it has to be on the line!
Remember, though, that in physics, slope has actual meaning and that it will have units. Slope is the rate of change for the object: how far it moves in y for every x. If the graph is a position (y) vs. time (x) graph, then slope means speed: slope = rise/run = (change of y)/ (change of x) = position/time = speed. Never find slope by counting the number of squares. That method works only when each square is equal to one (which is rare on real-life graphs).
The y-intercept, too, has actually physical meaning: it is the starting point. If an object starts at the measuring device, then it's y-intercept is 0 (meters, if talking position). If it starts 3 meters away, then its y-intercept is 3 m.
Realize that a graph that has units is talking about reality. Your number, then, should make sense. Some physical quantities cannot have a negative value: time duration, mass, volume, and length. You can't have a negative length or a negative amount of time! If your graph has a negative value for one of these you know your graph is wrong. Other quantities can have negative values like time (1200 A.D vs. 1200 B.C.) and position (in front vs. behind).
Copyright © 2004, C. Stephen Murray