Question

A curve has a equation y=f (x) write an expression for the slope of the secant line through the point p(x1, f(x1)) and q(x, f(x))

Answer 1

Given :  A curve has a equation y=f (x)  . slope of the secant line through the point p(x1, f(x1)) and q(x, f(x))

To find :   expression for the slope of the secant line through the point p(x1, f(x1)) and q(x, f(x))

Solution:

Slope of a line passing through two points ( x₁ , y₁) & (x₂ , y₂)

is given by

Slope = (y₂ - y₁)/(x₂ - x₁)   or  (y₁ - y₂)/(x₁ - x₂)

secant line through the point p(x1, f(x1)) and q(x, f(x))

Slope of the secant

= ( f(x) - f(x₁)) / (x - x₁)

or

( f(x₁) - f(x)) / (x₁ - x)

expression for the slope of the secant line through the point p(x1, f(x1)) and q(x, f(x))

( f(x) - f(x₁)) / (x - x₁)      or  ( f(x₁) - f(x)) / (x₁ - x)  

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