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Secant Line Calculator + Online Solver With Free Steps

The Secant Line Calculator is a very useful online tool for determining the slope of a secant line intersecting the defined curve at specified points. The slope can be used to derive the equation of the secant line through the given points.

This widget is easy-to-use and you can find the slope of the desired secant line on the curve just in seconds, avoiding the hassle of lengthy calculations. You just need to specify the function for which the slope is to be calculated and the reference points between which the secant line lies.

This calculator has certain design limitations due to which you have to add the function twice: once concerning x and in the next block concerning y as a variable.

What Is the Secant Line Calculator?

The Secant Line calculator is an online calculator that is used to determine the slope of the secant line on any curve between the specified points.

The Secant Line Calculator has been designed to calculate the slope of the secant line intersecting the curve with only one variable between the defined points. It finds the slope of the secant line between the two points using the Slope of a line formula that is given as:

\[ Slope = \dfrac{ f(b)\ -\ f(a) }{ b\ -\ a } \]

How To Use the Secant Line Calculator?

You can use the Secant Line Calculator by specifying the values of the point on curve ( x, y ) and entering the function first concerning x and then y. After clicking the submit button you can have your desired results.

Here are the detailed guidelines with steps on how to use the secant line calculator.

Step 1

First, enter the value of x in the specified tab displayed on the calculator.

Step 2

Now input the value of the variable y in the block titled y.

Step 3

Once you have added the value of x and y, enter the desired function regarding x in the blocks titled Function with ‘x’ as a variable.

Step 4

Afterward, add the function concerning y in the block titled Function with ‘y’ as a variable. The design limitation of the calculator requires the function to be added concerning both variables individually, as the calculator can deal with only one variable at a time.

Step 5

After filling all the desired information in the specified blocks, press the Submit button to calculate the slope of the secant line.

Step 6

The result will appear on the calculator, which will show the following two blocks:

Input Interpretation:

It shows the input entered by the user and perceived by the calculator. It includes the formula, value of x, the value of y, $f_o$ that is the function concerning x as a variable, and value of f1, which is the function concerning y as a variable.

Result:

The resulting block shows the calculated slope of the secant line on the curve.

The calculator tool uses the following formula to calculate the slope of the secant line at the backend:

\[ Slope = \dfrac{ f_1\ -\ f_o }{ y\ -\ x} \]

How Does the Secant Line Calculator Work?

The Secant Line Calculator works by using the values of x and y as a point on the curve and their corresponding functions to find the slope of the specified secant line.

To further clarify the result, let’s have a little insight about the slope of the function and a secant line.

Secant Line

The Secant Line is the line that lies on the curve and passes through any two specific points on the curve. it is a line that intersects the graph at two distinct points at least.

Slope of a Secant Line

The slope of the function is defined as the ratio of rising to run. In other words, the slope can also be defined as the rate of change of one variable y with respect to the other variable x.

There are multiple formulas for calculating the slope of a secant depending upon the data available. Let’s discuss all of them individually.

  • If two points ( x1, y1 ) and ( x2, y2 ) on the curve are given through which the secant line on the graph is running, then the formula for the slope of the secant line is given as:

\[ Slope = \dfrac{ y_2\ -\ y_1}{ x_2\ -\ x_1} \]

  • If the two points from which the secant line is passing are ( x, f(x)) and (y, f(y)), then the slope of the secant line is given as:

\[ Slope = \dfrac{ f(y)\ -\ f(x)}{ y\ -\ x} \]

This formula defines the average rate of change. The Secant Line Calculator also uses this formula to compute the slope of the secant line.

Solved Examples

Here are some examples that are solved using the Secant Line calculator to find the slope of the secant line on a curve.

Example 1

Determine the slope of the secant line on the following curve:

\[ f(x) = x^2 – 3x \]

The points are given as ( 2, f(2)) and (3, f(3)).

Use the Secant Line calculator to find the slope.

Solution

From the above-mentioned data, the value of x is given as:

x = 2 

The value of y is given as:

y = 3

The function with ‘x’ as a variable is given as:

\[ f(x) = x^2 -3x \]

The function with ‘y’ as a variable is given as:

\[ f(y) = y^2 -3y \]

Input the data in the calculator and press Submit button.

The result is shown below:

\[ Slope = \dfrac{ f(y)\ -\ f(x)}{ y\ -\ x} \]

Slope = 2 

Therefore, the slope of the secant line is 2.

Example 2

The parabola is given as:

\[ f(x) = 16x^2 \]

Calculate the slope of a secant line such that it passes through the points ( 3, f(3)) and (6, f(6)).

Solution

Input the following data in specified fields on the calculator:

x = 3 

y = 6 

\[ f(x) = 16x^2 \]

\[ f(y) = 16y^2 \]

Once you have entered the data, click on the Submit button.

The slope of the secant line passing through the given point is:

\[ Slope = \dfrac{ f(y)\ -\ f(x)}{ y\ -\ x} \]

 Slope = 144 

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