Which equation represents the line that passes through the points (6,-3) and (-4,-9) y+4= 3/5 (x+9) y+4= 5/3 (x+9) y-3= 3/5 (x+6) y+3= 3/5 (x-6)

D

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (6, - 3) and (x₂, y₂ ) = (- 4, - 9)

m = = =

using (- 4, - 9) or (6, - 3) for (a, b)

using (- 4, - 9), gives

y + 9 = (x + 4) ← not one of the options

using (6, - 3), gives

y + 3 = (x - 6) ← option D

the answer is simply just 6n add the two together as they have an n

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.