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

A secant line is also equivalent to the slope between two points.

Secant line = Slope = Average rate of change = m = \(\frac{\Delta a}{\Delta b} = \frac{b_{2}-b_{1}}{a_{2}-a_{1}} = \frac{f(a_{1})- f(a_{0})}{a_{1} -a_{0}} = \frac{f(t_{1})- f(t_{0})}{t_{1} -t_{0}}\)

Secant Line Formula Question:

Question: Evaluate the slope of the secant line:

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

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

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

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

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

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

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

The secant line equation is : \(b = \frac{ 1}{4}a + \frac{3}{4}\)

Here, the gradient is ¼.

Similarly, you can also study about equation of Tangent too

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