What is the equation of a line that has a slope of -2 and goes through (-1, -1)
y + 1 = -2(x + 1)
y - 1 = -2(x -1)
y + 1 = 2(x + 1)
y - 1 = 2(x - 1)

y + 11 = - 2(x + 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 2 and (a, b) = (- 1, - 1), thus

y - (- 1) = - 2(x - (- 1)), that is

y + 1 = - 2(x + 1)

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.