How do I find the slope of the line from the graph?

The slope is most easily defined as rise over run.

First, find a point you like because it is directly on the line and is where for example starting from the origin which you know should be always (0, 0).

Then find another point that is on the line and is perfectly aligned where on the graph is like (1, 2).

Then, as I said earlier, rise over run. So you climb up from for example the origin which is in the graph and climb up to the (1, 2) point. It should go up two units because it is increasing in intervals of 2 but has the notches in the half mark of 1.

So the rise is 2 because it climbed from 0 to 2.

The run is running from the 0 in the origin on the x-axis and running to the 1 because it is (1, 2) where it is in the form (x,y).

Since it is rise over run, the rise is 2 and the run is 1 so 2 over 1 is 2.

Hence the slope is 2.

Step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.