Question

Determine the slope of the secant line for the curve defined by the equation:
(attached below)

Answer 1

The slope of the secant line is basically the average rate of change from \(\bf x_0\) to \(\bf x_1\). This is given by:\[\bf m_{secant}=A.R.C.H|_{x_0}^{x_1}=\frac{ f(x_1)-f(x_0) }{ x_1-x_0 }\]

Answer 2

@mathcalculus Can you do that?

Answer 3

is that like the differentiation but in other terms?

Answer 4

@genius12

Answer 5

is it = to 1?

Answer 6

do we substitute just for it?

Answer 7

can we solve this together? @genius12

Answer 8

im stuck.

Answer 9

Ok I will solve step by step. Firstly, you should realise that this is essentially the slope formula which is:\[\bf m=\frac{ y_2-y_1 }{ x_2-x_1 }\]You remember that formula? @mathstudent55

Answer 10

yes

Answer 11

that's the formula to find the slope .

Answer 12

are you there?

Answer 13

Well that what this essentially is! It's the slope, of the secant line, and the secant line is the line that connects the two points on the graph when x = -5 to when x = -6. I'll draw the graph and show to you: