Choose the correct slope of the line that passes through the points (1, -3) and (3, -5) (whats the answer thats all i need to know)

You also need to know what "choose" means when you see it in a question.
It means "Here is a list. One of the things on this list is the answer.  Your job
is to figure out which one on the list is the right one, and choose it."

Seeing the word "choose" in your question, we know that wherever you
copied the question from, there was also a list of choices there.  But you
decided that you'd have a better chance of getting the right answer if you
didn't tell anybody the choices, so you posted the question without them.

The answer is  -1 .  I'd tell you how to figure it out, but I expect you wouldn't
read it. 

So I'll leave you with nothing.  All you have is the answer ... the least important
part of any school problem.  And plus, you haven't learned anything either.

Thanks for the points, though.

Answer

1 number

explanation

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.