Write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = -1.

y+1 = -1(x+10)

Step-by-step explanation:

The point slope equation of a line is

y-y1 = m(x-x1) where m is the slope  and (x1, y1) is a point on the line

y - -1 = -1 (x --10)

y+1 = -1(x+10)

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 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.