How can i find the averagee veloity and speed for a postion time graph

velocity is the derivative of the position function or the slope of the line....So

Choose two points on the graph. Subtract the "x-coordinates" (change in position), subtract the "t-coordinates" (change in time) and divide the first by the second,
v/t
is the slope of the line and the average velocity

i thought slope is the change in y over the change in x

yes you are correct.... I wrote the formula wrong

x/t instead of v/t
where x(position) is the dependent variable(y) and t is the independent variable(x)
sorry I know its confusing!! some people use s variable to represent the position
so:
delta s/delta t
where s(position) is the dependent variable(y-axis) and t is the independent variable(x-axis)
*where delta means change in s/change in t

Does that make more sense?

thank you verymuch

so would the average speed and velocity be the same thing

Your Welcome =D

Speed is the absolute value of velocity.
Velocity can be negative where as speed cannot. That is the only major difference but other than that they are the same!

This is all wrong.

Average Velocity is NOT the derivative.

Average Velocity defined= (positionfinal-positioninitial)/time