Determine the slope of a line that passes through A(-4, 7) and B(6,3)

Step-by-step explanation:

Use the formula:

Plug in the numbers (coordinates) given, like so:

Simplify:

-2/5

Step-by-step explanation:

The slope is found by

m= (y2-y1)/(x2-x1)

   = (3-7)/(6 - -4)

   = -4/(6+4)

   - 4/(10)

    = -2/5

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.