21) Write the equation for the line through two given points.
Passing through (0, -1) and (2, 3)

Point Slope: (y + 1) = 2x

Slope Intercept: y = 2x - 1

Step-by-step explanation:

I'll do it in two forms.

Slope = (3 + 1) / (2 - 0) = 2

Point - Slope: (y + 1) = 2x

Slope Intercept: y = 2x + b

-1 = b

y = 2x - 1

345

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.