# Thread: Slope of Secant Line

1. ## Slope of Secant Line

The slope of the secant line can be written this way:

f(x + h) - f(x)/h.

For both questions below, express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.

(1) f(x) = -3x + 2

(2) f(x) = 1/x

Also, what exactly is the slope of the secant line?

What is a secant line anyway?

2. Originally Posted by symmetry
The slope of the secant line can be written this way:

f(x + h) - f(x)/h.

You need to put the brackets in this properly:

[f(x + h) - f(x)]/h.

For both questions below, express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.

(1) f(x) = -3x + 2

[f(x + h) - f(x)]/h=[(-3(x+h) + 2)-(-3x + 2)]/h=[-3h]/h=-3

(2) f(x) = 1/x

[f(x + h) - f(x)]/h=[(1/(x+h)-1/x]/h=[(x-(x+h))(x(x+h))]/h=-1/(x(x+h))

Also, what exactly is the slope of the secant line?

What is a secant line anyway?
Definition of a secant line can be found here.

As it is a line its slope is defined as the tan of the angle that
the line makes with the horizontal.

RonL

3. Originally Posted by symmetry
The slope of the secant line can be written this way:

f(x + h) - f(x)/h.

For both questions below, express the slope of the secant line of each function in terms of x and h. Be sure to simplify your answer.

(1) f(x) = -3x + 2

(2) f(x) = 1/x

Also, what exactly is the slope of the secant line?

What is a secant line anyway?
Expanding on what CB said;

It's known as the difference quotient of f.

Given (x, f(x)) and (x + h, f(x + h)), then y = f(x) can be given by:

[f(x + h) - f(x)]/[(x + h) - x] = [f(x + h) - f(x)]/h, where h does not equal 0.

It's also the derivative (slope), which I recall you telling TPH you hadn't got to yet. Or, (y_2 - y_1)/(x_2 - x_1), or (delta y)/(delta x).

4. ## ok

Thank you both for your replies and the great math data given to me for my study time this coming week.