Slope of the Secant Line Formula

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 = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Slope of a secant line at a given interval is:

\(m_{sec}= \frac{f(x+\bigtriangleup x)- f(x)}{\bigtriangleup x}\)

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 = \(\frac{\Delta a}{\Delta b} = \frac{b_{2}-b_{1}}{a_{2}-a_{1}}\)

= \(\frac{f(-4)- f(1)}{(-4)-1}\)

= \(\frac{(\frac{-1}{4})- (1)}{(-5)}\)

= \(\frac{(\frac{-5}{4})}{(-5)}\)

= \(\frac{ 1}{4}\)

Here, the gradient is ¼.

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

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