how to find the slope of a line

So now you have a graph. Yippy.
What can you use it for?
You can use it to find the speed of the moving object at any time. Physics books refer to this as "instantaneous speed".
It should be clear by now that when an object moves at a constant speed, its distance/time graph shows a straight line. The steeper the line, the higher the speed.

You should also have a a feeling that much of our motion is not at one speed. We are often accelerating (+ or -), even when we are trying to maintain one speed on the road.

Let's talk about those straight lines first...

Speed=distance/time, OUR GRAPHS show us these two things, so they can give us speed.
If you find the slope of the line (slope=steepness, or grade, etc.) you find the speed.

Look at this example...


	This image shows motion at a constant speed.
	The speed is given by the slope of the line. Slope is defined as DY/DX and in our case, it's Ddistance/Dtime. Here, I drew a triangle on the graph using two points on the line. So, X=3-1=2 and Y=3-1=2, so 2/2=1block/second
	The speed here is higher. You can tell because the line is steeper.What is the speed? (4-0)/(2-0)=2blocks/second
	Here, the line doesn't nicely line up with the gridlines, so we must think just a little more...(see below)
	(4-0)/(3.5-0)=1.14blocks/sec

The nice thing is that we can pick any 2 spots to use when finding slopes. I like to pick spots where the line intersects grid intersections to keep the math easier, but either way this process is easy. Look and see that the triangle formed always has the same shape.

Look HERE for a quick description about how to find the slope of a line. Look here for PRACTICE in finding slopes.