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 =Â \(\begin{array}{l}\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\end{array} \)
Slope of a secant line at a given interval is: \(\begin{array}{l}m_{sec}= \frac{f(x+\bigtriangleup x)- f(x)}{\bigtriangleup x}\end{array} \) |
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 =
\(\begin{array}{l}\frac{\Delta a}{\Delta b} = \frac{b_{2}-b_{1}}{a_{2}-a_{1}}\end{array} \)
=
\(\begin{array}{l}\frac{f(-4)- f(1)}{(-4)-1}\end{array} \)
=
\(\begin{array}{l}\frac{(\frac{-1}{4})- (1)}{(-5)}\end{array} \)
=
\(\begin{array}{l}\frac{(\frac{-5}{4})}{(-5)}\end{array} \)
=
\(\begin{array}{l}\frac{ 1}{4}\end{array} \)
Here, the gradient is ¼.
Similarly, you can also study about the equation of Tangent too
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