Now...it's the Slope of Tangents and Instantaneous Rate of Change

In the previous post, I explained all about slopes of a secant on a graph. Just refreshing, secant line is a line connecting any 2 points on a graph. Whereas, a tangent line is a line passing through only 1 point on a graph.

The point on the graph is where the instantaneous rate of change takes place ; that is, the
change in y ÷change in x without an interval
Unlike the slope of a secant line, we have 2 reference points to determine its slope. How about a tangent line where there is only ONE point to refer to?

Steps:
1. Draw a tangent line through the point of reference ; a line cutting through only 1 point on the graph. NOTHING MORE THAN THAT ONE POINT!

2.  As you can see, the tangent cuts 1 point on the graph. Now, take any 2 points from the yellow straight line, a.k.a the tangent line, and find its slope, just the way you found the slope for a secant line.
3. When you have found your slope of the tangent line, this is called the instantaneous rate of change at the red point when x = ...

Note : You have to know the secant line well enough first to be able to master the tangent line questions.

See you!