How do I find rate of change.

Question

How do I find the rate of change from a graph (8th grade algebra)?

Answer 1

rate of change is the slope of the tangent line to the curve

if the "curve" is a straight line, the rate of change is the slope of the straight line, take 2 points on the line and divide the change in y coordinates by the corresponding change in x coordinates

If it's not a linear equation, the instantaneous rate of change is the slope of the tangent line at a point

the average rate of change between two points the curve is the slope of a secant line, the line connecting the two points

If you the graph is a parabola, such as y=x^2

the instantaneous rate of change is 2x, the slope of a tangent line at a point (x,y). If you want the rate of change when (x,y) = (2,4) then it's 2(2) = 4

if you want the average rate of change from (0,0) to (2,4)

draw a line connecting those two points. the slope of that line is the average rate of change 4/2 = 2