What is the slope of the line that passes through the points (-6,1) and (4,-4)

Slope of the line is -0.5

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1); Here x1 = -6, y1 = 1, x2 = 4 and y2 = -4

⇒ m = (-4 - 1)/(4 - -6)

       = -5/10 = -1/2 = -0.5

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.