**Math Calculators** ▶ Slope Calculator

An online slope calculator helps to find the slope (m) or gradient between two points \(A\) \((x_1, y_1)\) and \(B\) \(y_1, y_2)\) in the Cartesian coordinate plane. This slope of a line calculator will take two points to calculate \((m)\) and \(y-intercept\) of a line.

In mathematical terms, 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 \((m)\).

There are four different types of slope that all are depending on the direction of the line. Read on!

- If the line goes up to the right, it is said to be a positive slope or gradient
- If the line goes down to the right, the it is said to be a negative slope or gradient
- A horizontal line has a slope \((m)\) of zero
- A vertical line has an undefined slope or gradient

You can try our slope finder that allows you to find both \(X-intercept\) and \(Y-intercept\) from the given points.

Give a try to this best midpoint calculator online that enables to find the distance & midpoint of a line segment and also shows you the step-by-step complete calculations.

Also, the free slope intercept form calculator by calculator-online helps to find slope-intercept form equation from given points.

This calculator allows you to perform calculations corresponding to the slope and different other parameters:

- You can readily find \((m)\) or gradient of a line that passes through 2 points
- It assists you to solve a coordinate for a given point, \((m)\) or angle \((θ)°\), and distance from a point
- It helps you to find the \(x\) or \(y\) of a point for a given another point and the \((m)\) or angle \((θ)°\)
- You can readily find \((m)\) or angle for a given parameters
- It allows you to find the slope of the given line

Well, in this post, we are going to tells you what is the slope formula is, how to find it (manually) or by using a calculator, and much more.

Also, use this free point slope form calculator online that displays the equation of a line by using the coordinate points and \((m)\) of the line.

$$ Slope (m) = \frac {ΔY}{ΔX} or \frac {y_2 – y_1} {x_2 – x_1} $$

**In this slope equation;**

\(m\) = \(slope\)

\(ΔY\) = \((y_2 – y_1)\)

\(ΔX\) = \((x_2 – x_1)\)

Teachers often use different words for the y-coordinates and the x-coordinates:

- Some refer to \(y-coordinates\) as the \(rise\) and \(x-coordinates\) as the \(run\)
- Others consider the \(Δ\) notation and refer to the \(y-coordinates\) as \(Δy\), and \(x-coordinates\) as \(Δx\)

Let’s use the above formula to find the slope that goes through the points \((2, 1)\) and \((4, 7)\).

**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.

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:**

- 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

**Output:**

Once you entered all the above parameters, then simply hit the calculate button, the 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

**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 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

**Output:**

Once done, then simply hit the calculate button:

- 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: \(y = mx + b\)

**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 calculator
- 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

**Output:**

Once you added all the above-parameters, hit the calculate button, 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: \(y = mx + b\)

**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

**Output:**

Once you filled the all parameters, then simply hit the calculate button, this calculator will generate:

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

**Input:**

- You have to enter a line equation into the given fields of this calculator

**Output:**

Once you entered the line equation, then hit the calculate button, this will generate:

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

You can find slope of a line by comparing any 2 points on the line. Look at the given example for better understanding:

**Slope Formula: \(m = \frac {y_2 – y_1}{x_2 – x_1}\)**

**For Example:**

The line passes through the points \((3, 2)\) and \((7, 5)\), how to find slope of a line?

**Solution:**

\(m = ((5 – 2))/((7 – 3))\)

\(m = ((3))/((4))\)

This calculator for slope helps you in finding the gradient or \((m)\) and shows you the slope graph corresponding to the given points.

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

\( Distance (d) = \sqrt {(x₂ – x₁)^2 + (y₂ – y₁)^2 } \)

You can find the angle of a line in degree from the inverse tangent of the slope \((m)\).

**The Formula is:**

\(θ = tan-1(m)\)

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:**

\(m = tan(θ)\)

For Example: If \(angle = 90\), then the slope is equal to \(tan (90)\).

As we know, the linear equation: \(y = mx + b\), or sometimes \(y = mx + c\),

**Slope Equation of a Line:**

\(y = mx + b\), or sometimes \(y = mx + c\),

where;

- \(m\) = slope (said to be the amount of rise over run of the line)
- \(b\) = \(y-axis\) intercept (said where the line crosses over the \(y-axis\)

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: \(y – mx = b\)

**Example:**

Want to calculate the slope-intercept equation for a line, which includes the two points i:e \((7, 4)\) and \((1, 1)\), let’s take a look!

**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 calculator show the same answer for these given parameters.

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:

\(Δy = y_2 – y_1\)

Let’s take a look!

**Example:**

A line is passes through the point \((7,5)\) and it has a slope of \(9\). What is the equation?

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!

Slope as a Percentage:

Yes, gradient or \((m)\) can be determined as a percentage that is calculated in much the same as the gradient. Just stick to the following steps to attain best!

- First of all, you have to convert the rise and run to the same units
- Then, you have to divide the rise by the run
- Now, you ought multiply this number by \(100\), means you have the percentage slope

**For instance:**

\(“2”\) rise divided by \(“24”\) \(run\) = \(.083 \times 100\) = an \(8.3%\) slope.

Simply, \(1%\) as a decimal is \(0.01\) and hence the slope is referred to as \(0.01\). Means that for a run of pipe of a certain length the rise should be \(0.01\) times the length. Thus a, for instance, as the length of the run is \(80\) feet that is expressed as \(80 \times 12 = 960\) inches the rise should be \(0.01 \times 960\) \(= 9.6 inches\).

\(1/4″\) per foot pitch equals to \(2%\) \((percent)\), and remember that it is not expressed as \(2\) degrees.

\(Slope percent\) \(=\) \(\frac {8 feet}{40 feet} \times 100 = 0.20 \times 100 = 20%\)

In this equation, the slope is expressed as \(−4\) as this equation is in standard linear form that is \(y=mx+c\), where \(m\) is the slope.

Simply, you ought to use a protractor and trigonometry!

When it comes to a straight line with a slope of \(-1\), it moves down at a \(45°\) angle as it moves to the right.

All you need to simply divide the elevation change in feet by the distance of the line that you drew (after converting it to feet). Then, you need to multiply the resulting the number by 100 to find a percentage value equal to the percent slope of the hill.

You need to use the Pythagorean Theorem to calculate the length of a slope, where the vertical distance is said to be rise and the horizontal distance indicated as the \(run: rise^2 + run^2 = slope length^2\).

The maximum running slope allowed is \(1:20\) for the parts of an accessible route that aren’t a ramp. Simply, it means that for every inch of height change there should be at-least \(20in\) of route run. Also, the distance from the bottom edge of the level to the surface will not be more than \(1.2 inches (1.2:24 = 1:20)\).

When it comes to finding the slope \((m)\) of a curve at a particular point, you need to differentiate the equation of the curve. If the given curve is \(y = f(x), y = f(x)\), you ought to evaluate \(\frac{dy}{dx}\) and substitute the value of \(x\) to calculate the slope.

When you’re going to find the slope of real-world situations, typically it is referred to as the rate of change. Remember that “Rate of change” indicates same as \(“m”\). If you are asked to find the rate of change, simply use the \((m)\) formula or make a slope triangle.

Remember that slope is a measure of steepness. Some real-life examples of slope are mentioned-below:

- To building roads when you need to know how steep the road will be
- Skiers/Snowboarders consider the slopes of hills as it helps to judge the dangers, speed, etc
- When it comes to constructing wheelchair ramps, slope is a major consideration
- When it comes to building stairs, you should have to consider the slope so that they are not too steep to walk on
- In art, slopes of the line should considered as it assists to decide what would be the most aesthetically pleasing to eye

A \(10%\) slope indicates that, for every \(100 ft (feet)\) of horizontal distance, the altitude simply changes by \(10 ft (feet): {10 ft over 100 ft} \times 100 = 10%\).

You should have to integrate the equation & subtract the lower bound of the area from the upper bound to find the area under a slope. When it comes to linear equations:

- First of all, you need to put the equation into the form \(y=mx+c\)
- Now, you ought to write a new line where you ought to add \(1\) to the order of the \(x\) (for instance, \(x\) becomes \(x2, x2.5\) becomes \(x3.5\)
- Very next, you need to divide slope \((m)\) by the new number of the order and place it in front of the new \(x\)
- Then, you ought to multiply the \(c\) by \(x\) and simply add this to the new line
- Now, you ought to solve this new line twice: one where \(x\) is indicated as the upper bound of the area you need to find and second where \(x\) is indicated as the lower bound
- Finally, subtract the lower bound from the upper bound
- Congrats, you calculated area under a slope

Luckily, you come to know how to find the slope manually in legitimate ways. The amazing thing is that there is no need to remember these formulas, you just have to account the above \((m)\) slope calculator to find gradient or \((m)\).

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) –

From the source of mathblog – An Introduction To Algebra – Solve for Slope with Two Points on a Line

The coolmath provided you with – Algebra – Page 1 of 2 – Finding the Slope of a Line from the Equation – The World of Math

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