What is the equation of the line that passes through the point (-6,-6)(−6,−6) and has a slope of 2/3?

y = 2/3 x -2

Step-by-step explanation:

We have a point and a slope

y = mx+b

The slope, m, = 2/3

y = 2/3 x+ b

The point is (-6,-6)

Substitute this into the equation to solve for b

-6 = 2/3 (-6) +b

-6 = -4+b

Add 4 to each side

-6+4 = -4+4+b

-2 =b

Substitute into the equation

y = 2/3 x+ b

y = 2/3 x -2

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.