Slope Calculator

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.

What Is Slope?

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)

Slope Formulas:

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:

• y – intercept can also be termed rise
• x – intercept can also be called as the run
• Others consider the Δ notation and refer to the y−coordinates as Δy, and x−coordinates as Δ

 

 

How to Find Slope With 2 Points?

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:

$$ Slope \left(m\right) = \frac {y_2 – y_1} {x_2 – x_1} $$

Distance Between Two Points:

The formula to determine the distance (D) between 2 different points is:

$$ Distance (d) = \sqrt {(x_2 – x_1)^{2} + (y_2 – y_1)^{2}} $$

Slope to Angle Conversion:

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).

Angle to Slope Conversion:

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.

How to Find the Slope of an Equation?

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.

Equation of a Line From Two Coordinates:

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: \(y – mx = b\)

Find a Point Given 1 Point, Slope(m), and Distance:

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 Delta (Δ) of x and y:

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:

$$ Δy = y_2 – y_1 $$

How to Find Slope and other Related Parameters?

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.

How to Find Slope With Our 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:

Two Points:

Input:

• First of all, you ought to select the ‘two points’ option from the drop-down menu of this slope solver for 2 points
• Very next, you have to enter the \(X_1\) value into the designated field
• Then, you have to enter \(Y_1\) value into the designated field
• Right after, you have to enter \(X_2\) value into the designated field
• Now, you have to enter \(Y_2\) value into the designated field
• Once you entered all the above parameters, then simply hit the calculate button

Output:

The best slope from two points calculator helps to find slope from two points and generate:

• Slope \((m)\)
• Percentage Grade
• Angle \((θ)\)
• Distance
• \(ΔX\)
• \(ΔY\)
• \(X – Intercept\)
• \(Y – Intercept\)
• Slope-Intercept: \(y = mx + b\)
• Graph For a 2 points

One Point, Slope (m) or Angle (θ)° & Distance:

Input:

• First of all, you ought to select the ‘One Point, Slope \((m)\) or Angle \((θ)°\) & Distance’ from the drop down menu
• Then, you have add the value of \(X_1\) into the given field of the above graphing slope calculator
• Very next, you have to add the value of \(Y_1\) into the given field
• Now, you ought to add the value for Slope \((m)\) or Angle \((θ)°\) into the given field of this tool
• Then, you ought to add the value of distance into the designated field
• Once done, then simply hit the calculate button

Output:

The slope of line calculator does the following calculations in this case:

• Right \(X_2\)
• Right \(Y_2\)
• \(ΔX\)
• \(ΔY\)
• Graph for a right \(X_2\) and right \(Y_2\)
• Left \(X_2\)
• Left \(Y_2\)
• \(ΔX\)
• \(ΔY\)
• Graph for a left \(X_2\) and left \(Y_2\)
• Slope \((m)\)
• Percentage Grade
• Angle \((θ)\)
• Distance
• \(X – Intercept\)
• \(Y – Intercept\)
• Slope-Intercept: \(y = mx + b\)

One Point, X or Y & Slope (m):

Input:

• At first, you ought to enter the value of \(X_1\) into the given field
• Then, you ought to add the \(Y_1\) value into the given box of the graph calculator slope
• Very next, you ought to \(X_2\) or either \(Y_2\) into the given field
• Now, you ought to add the Slope \((m)\) or either Angle \((θ)°\) into the designated box
• Once you added all the above-parameters, hit the calculate button

Output:

This y=mx+b calculator will generate:

• \(X_2\)
• \(Y_2\)
• \(Δx\)
• \(Δy\)
• Slope \((m)\)
• Percentage Grade
• Angle \((θ)\)
• Distance
• \(X – Intercept\)
• \(Y – Intercept\)
• Slope-Intercept: \(y = mx + b\)

One Point & Slope (m):

Input:

• At first, you have to enter the value of \(X_1\) into the given field
• Now, you have to add the value of \(Y_1\) into the given box
• Then, simply, you have to enter \((m)\) or either Angle \((θ)°\) into the given field of slope finder
• Hit the calculate button

Output:

The find slope calculator will generate:

• Slope \((m)\)
• Percentage Grade
• Angle \((θ)\)
• \(X – Intercept\)
• \(Y – Intercept\)
• Slope-Intercept: \(y = mx + b\)

Line:

Input:

• You have to enter a line equation into the given fields of this calculator
• Tap the calculate button

Output:

This free slope calculator from equation will generate:

• Slope \((m)\)
• Percentage Grade
• Angle \((θ)\)
• \(X – Intercept\)
• \(Y – Intercept\)
• Slope-Intercept: \(y = mx + b\)

 

References:

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) –

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