When one end or side of a surface is at a higher side than another, It’s called Slope.

A straight line which joins two points on a function is a Secant line.

Secant line slope formula

Slope of a secant line through two points =

\begin{array}{l} \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \end{array}

Slope of a secant line at a given interval is:

\begin{array}{l} m_{s e c} = \frac{f (x + △ x) - f (x)}{△ x} \end{array}

Secant Line Formula Question:

Question: Evaluate the slope of the secant line:

f(x) = 1/x, through the points: (-4, f(-4)) & (1,f(1))?

Solution: The slope formula for secant line is same as slope of any line.

m =

\begin{array}{l} \frac{Δ a}{Δ b} = \frac{b_{2} - b_{1}}{a_{2} - a_{1}} \end{array}

\begin{array}{l} \frac{f (- 4) - f (1)}{(- 4) - 1} \end{array}

\begin{array}{l} \frac{(\frac{- 1}{4}) - (1)}{(- 5)} \end{array}

\begin{array}{l} \frac{(\frac{- 5}{4})}{(- 5)} \end{array}

\begin{array}{l} \frac{1}{4} \end{array}

Here, the gradient is ¼.

Similarly, you can also study about the equation of Tangent too

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