Math Calculators ▶ Slope Calculator
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Table of Content
This slope calculator helps to find the slope (m) or gradient between two points \(A\left(x_1, y_1\right)\) and \(B\left(x_2, y_2\right)\) in the Cartesian coordinate plane.
This find the slope of a line calculator will take two points to let you know how to calculate slope (m) and y−intercept of a line.
In the light of mathematical analysis:
“The slope or gradient of the line is said to be a number that defines both the direction and steepness of the line.”
Typically, it is denoted by the letter (m)
Wondering about what is the slope formula? Do not worry at all as we will be mentioning then right below. Now you could easily determine the slope graph online by subjecting to the following equation to find slope:
$$ Slope \left(m\right) = \frac {ΔY}{ΔX} $$
Or
$$ Slope \left(m\right) = \frac {y_2 – y_1} {x_2 – x_1} $$
In this slope equation;
\(m = slope\)
\(ΔY = (y_2–y_1)\)
\(ΔX = (x_2–x_1)\)
This best y intercept calculator also goes for using the same formula to compute the value of the steepness of the y line in a fragment of seconds. What are your thoughts on it?
Note:
Here you can recall these parameters by using different names such as:
You can find slope of a line by either comparing any 2 points on the line or using this free graph slope calculator from points. So if you are seeking how to find slope from two points, revise the slope formula again:
$$ Slope \left(m\right) = \frac {y_2 – y_1} {x_2 – x_1} $$
The formula to determine the distance (D) between 2 different points is:
$$ Distance (d) = \sqrt {(x_2 – x_1)^{2} + (y_2 – y_1)^{2}} $$
You can find the angle of a line in degree from the inverse tangent of the slope \((m)\).
Equation:
$$ θ = tan^{-1}\left(m\right) $$
OR \(θ = arctan \frac {(ΔY)}{(ΔX)}\)
Where;
\(m\) = slope
\(θ\) = angle of incline
For Example:
If the slope is 5, the angle of an incline in degrees is tan-1(5).
Simply, all you have to remember is that the slope is equal to the tangent of the angle.
Equation:
$$ m = tan\left(θ\right) $$
For Example:
If \(angle = 90\), then the slope is equal to \(tan (90)\).
For instant outcomes, you may use this free slope equation calculator.
When it comes to the inclination of the equation given, it actually means what is the slope of the line that represents the expression. Let’s consider the generic equation of the line:
$$ y = mx + c $$
Where:
m = slope of the line
c = point where the line intersects the y axis
This best slope graphing calculator also simplifies the given form of the line equation in moments.
If you want to calculate the equation of a line from two coordinates \((x_1, y_1)\) and \((x_2, y_2)\) manually, then you have to stick to the following steps:
Step # 1:
First of all, you have to use the \((m)\) formula to calculate the slope \(\frac {(y_2 – y_1)}{(x_2 – x_1)}\)
Step # 2:
Now, you ought to calculate where the line intersects with the \(y-axis\):
To do so,
You ought to enter one of the coordinates into this slope equation: \(y – mx = b\)
No doubt, points on a line can be readily solved given the slope of the line and the distance from another point. The formulas to find x and y of the point to the right of the point are as:
$$ x_2 = x_1 + \frac{d}{\sqrt(1 + m^2)} $$
$$ y_2 = y_1 + m \times \frac{d}{\sqrt(1 + m^2)} $$
The formula’s to find x and y of the point to the left of the point are as:
$$ x_2 = x_1 + \frac{-d}{\sqrt(1 + m^2)} $$
$$ y_2 = y_1 + m \times \frac{-d}{\sqrt(1 + m^2)} $$
The symbol \(Δ\) is used to express the delta of \(x\) and \(y\), simply, it is the absolute value of the distance between \(x\) values or \(y\) values of \(2\) points.
The \((Δ)\) delta of \(x\) can be determined using the formula:
$$ Δx = x_2 – x_1 $$
The \((Δ)\) delta of y can be determined using the formula:
$$ Δy = y_2 – y_1 $$
Right here, we will be taking you through a series of examples that will highlight the map structure of slope and other entities related to it! Just Stay Focused!
Example # 01:
Find slope with two points that are:
$$ \left(2, 1\right) \hspace{0.25in} and \hspace{0.25in} \left(4, 7\right)
Solution:
Step # 1:
First of all, you have to identify the values of \(x_1, x_2, y_1\) and \(y_2\).
\(x_1) = 2\)
\(y_1 = 1\)
\(x_2 = 4\)
\(y_2 = 7\)
Step # 2:
Now, you have to put the above values into the formula:
\((m)\) = \(\frac {y_2 – y_1}{x_2 – x_1} = \frac {7 – 1} {4 – 2} = \frac {6}{2} = 3\)
Step # 3:
Get check the result and you ought to make sure that this slope make sense by thinking about the points on the coordinate plane.
Also, you can try this formula (m=y2-y1/x2-x1 calculator) to find the slope of the line or given coordinates.
Example # 02:
The line passes through the points \((3, 2)\) and \((7, 5)\), how to find the slope of a line?
Solution:
Finding slope from two points as follows:
\(m = ((5 – 2))/((7 – 3))\)
\(m = ((3))/((4))\)
Example # 03:
How to find slope with two points given as under:
$$ \left(5, 9\right) \hspace{0.25in} and \hspace{0.25in} \left(2, 0\right)
Solution:
Now you must be wondering about what is slope for given set of coordinates. But do not worry as we will be using the same formula of slope as aforementioned.
$$ Slope \left(m\right) = \frac {y_2 – y_1} {x_2 – x_1} $$
$$ Slope \left(m\right) = \frac {0 – 9} {2 – 5} $$
$$ Slope \left(m\right) = \frac {9} {–3} $$
$$ Slope \left(m\right) = -3 $$
You can also verify the answer by using our best slope calculator graph that will let you know statistics about the graph inclination in moments.
Example # 04:
A line is passes through the point \((7,5)\) and it has a slope of \(9\). What is the equation?
Solution:
Well, we can easily calculate \(‘b’\) from this equation:
\(b = y – mx\)
Now, let’s plug-in the values into the above equation:
\(b = 5 – (9)(7)\)
\(b = -58\)
Very next, we plug-in the value of \(‘b’\) and the slope into the given equation:
\(y = mx +b\)
\(y = 9x -58\)
Also, you can use the above slope finder to perform instant calculations instead of sticking to these manual calculation steps!
Example # 05:
Calculate the slope-intercept equation for a line, which includes the two points i:e \((7, 4)\) and \((1, 1)\).
Solution:
Step # 1:
Slope \((m)\) = \(\frac {ΔY}{ΔX} = \frac {(1 – 4)}{(1 – 7)} = \frac {(-3)}{(-6)}\)
Slope \((m)\) = \(\frac {-3}{-6} = \frac {1}{2}\)
Step # 2:
So, now, using one of the original coordinates \((7, 4)\), we readily find the \(y-axis intercept (b)\) using the slope formula:
\(y – mx = b\)
\(y=4, m=\frac {1}{2}, x =7\)
\(y – mx = b\)
\(b= .5\)
The slope equation for this line is as:
\(y = .5x + .5\)
This line crosses the \(y-axis\) at \(.5\) and has a slope of \(.5\), so it referred to as this line rises one unit along the \(y-axis\) for every \(2\) units it moves along the \(x-axis\). Also, our online find the equation of a line calculator show the same answer for these given parameters.
Given the slope of the line, you can also determine the equation of this line by using another equation of a line calculator.
The slope formula calculator uses the simple and smart formula for \((m)\) or gradient to do calculations.
You can perform calculations with the following:
Input:
Output:
The best slope from two points calculator helps to find slope from two points and generate:
Input:
Output:
The slope of line calculator does the following calculations in this case:
Input:
Output:
This y=mx+b calculator will generate:
Input:
Output:
The find slope calculator will generate:
Input:
Output:
This free slope calculator from equation will generate:
From Wikipedia, the free encyclopedia – what is the slope – Examples and much more!
The Source of Mathplanet recently updated – Pre-Algebra / Graphing and functions / – how to find (m) –
Other Languages: Steigung Berechnen, 勾配計算, Calcul Pente, Calculo De Inclinação, Calcular Pendiente, Calcolo Pendenza, Калькулятор Уклонов, Výpočet Sklonu, Kattokaltevuus Laskuri, Eğim Hesaplama, Kalkulator Nachylenia, Kalkulator Kemiringan.