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Slope Calculator

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Y₁

X₂

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Slope (m)

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Angle (θ)°

Distance

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y

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Table of Content
 1 What Is The Slope? 2 The Slope Formula 3 Slope Calculator By Calculator-Online 4 Our Slope Calculator Works 5 How To Find The Slope of a Line? 6 How to Find The Distance Between 2 Points? 7 How to Convert Slope to Angle? 8 Words By Calculator-Online
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The slope calculator is the efficient tool that helps to find slope & distance between two points, slope & angle, x and y intercept, and slope intercept form for a given parameters. This slope finder sometimes also referred to as a slope of a line calculator as it allows you to calculate slope of the given line by using simple slope formula.

Well, in this post, we are going to tells you what the slope formula is, how to find slope (manually) or by using our slope calculator and everything that you need to know about the slope.

What Is The Slope?

Slope definition is very simple; it is said to be a measure of the difference in position between two points on a line. According to the mathematician, if the line is plotted on a 2-dimensional graph, then the slope is something that shows how much the line moves along the x-axis and the y-axis between those 2 points. Yes, finding slope becomes easy with the ease of our reliable slope point calculator – this tool uses a simple slope equation to find slope.

The slope is an important concept in mathematics that is usually used in basic or advanced graphing like linear regression; the slope is said to be one of the primary numbers in a linear formula.

What Are The Types of Slope?

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

Let’s digging deeper!

Positive Slope:

If the y-values are increasing as the x-values increase, it referred to as the line has a positive slope. If you trace the line by using your finger, means from left to right (same as you read a book), the line will go up to the right.

Negative Slope:

If the y-values are decreasing, it referred to as the line has a negative slope. If you trace the line by using your finger, means from left to right (same like the direction that you read a book), the line will go down to the right.

Slope of Zero:

If the y-values are not changing as x increases, it is indicated as the line will have a slope of 0. Remember that if the line is horizontal anytime (flat from left to the right), the slope is said to be zero. This would refer to as a situation where there is not any change.

Undefined Slope:

As mentioned earlier a vertical line has an undefined slope. Remember that in such situation, the y-values are changing, but when it comes to the x-value, it always stays the same. You can take a look on the definition of slope that demonstrates the amount of horizontal change is in the denominator of a fraction. In mathematical terms, you can’t have a 0 in the denominator. It doesn’t make any legitimate sense to divide by 0 so it is said that the slope of a vertical line is undefined. Remember that there is not a slope for these types of lines.

The Slope Formula:

Slope (m) = ΔY/ΔX

In this slope equation;

M = slope

ΔY = (y₂ – y₁)

ΔX = (x₂ – x₁)

Using the Slope Formula:

Let’s use the above formula equation for slope 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 x₁, x₂, y₁ and y₂.

x₁ = 2

y₁ = 1

x₂ = 4

y₂ = 7

Step # 2:

Now, you have to put the above values into the slope formula to find the slope:

Equation for slope = y₂ – y₁/ x₂ – x₁ = 7 – 1/ 4 – 2 = 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.

Luckily, you can find the slope or gradient between two points in the Cartesian coordinate system with the ease of our online point slope calculator. No doubt, finding the slope becomes easy with this slope finder, it will assist you in the following ways:

• You can readily find slope or gradient of a line that passes through 2 points
• It assists you to solve a coordinate for a given point, slope(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 slope(m) or angle (θ)°
• You can readily find slope or angle for a given parameters
• This simple slope of a line calculator allows you to find the slope of the given line

How to Find Slope With The Slope Calculator:

The slope formula calculator uses the simple and smart formula for slope that helps you in finding the slope. Our slope finder is 100% free and feel-hassle free to account this calculator for slope.

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 calculator for two points
• Very next, you have to enter the X₁ value into the designated field
• Then, you have to enter Y₁ value into the designated field
• Right after, you have to enter X₂ value into the designated field of this slope intercept form calculator
• Now, you have to enter Y₂ value into the designated field

Output:

Once you entered all the above parameters, then simply hit the calculate button, the slope calculator for two points will generate:

• Slope(m)
• 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 X₁ into the given field of the above calculator
• Very next, you have to add the value of Y₁ 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, this slope intercept form calculator will provides you with:

• Right X₂
• Right Y₂
• ΔX
• ΔY
• Graph for a right X₂ and right Y₂
• Left X₂
• Left Y₂
• ΔX
• ΔY
• Graph for a left X₂ and left Y₂
• Slope (m)
• 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 X₁ into the given field of this slope finder
• Then, you ought to add the Y₁ value into the given box of the calculator
• Very next, you ought to X₂ or either Y₂ 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 point slope calculator will generates:

• X₂
• Y₂
• Δx
• Δy
• Slope (m)
• 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 X₁ into the given field of slope formula calculator
• Now, you have to add the value of Y₁ into the given box of the calculator for slope
• Then, simply, you have to enter Slope (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 slope (m) calculator will generates:

• Slope (m)
• 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

Output:

Once you entered the line equation, then hit the calculate button, this slope of a line calculator will generates:

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

Thankfully, you come to know how to find the slope using the simple slope of a line formula.

How To Find The Slope of a Line Given 2 Points?

You can find slope of a line by comparing any 2 points on the line. A point is said to be as an X and Y value of a Cartesian coordinate on a grid. Slope; represented as m, it can be found using the slope formula that is given:

Slope Formula: m = ((y2 – y1))/((x2 – x1))

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))

How to Find The Distance Between 2 Points?

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

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

How to Convert Slope to Angle?

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(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).

How to Convert Angle to Slope?

You can also be able to convert an angle in degrees into a slope. 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).

Using The Slope Intercept Form – how do you find y=mx+b?

Slope Intercept Form Equation: y = mx + b, or sometimes y = mx + c,

Slope Intercept Form Equation:

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)

Find the Slope Intercept Form Equation From Two Coordinates:

To calculate the slope intercept form equation from two coordinates (x₁, y₁) and (x₂, y₂), then you have to stick to the following steps:

Step # 1:

First of all, you have to use the slope formula to calculate the slope (y₂ – y₁) / (x₂ – x₁)

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 of Slope-Intercept Equation:

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) = ΔY / ΔX = (1 – 4) / (1 – 7) = -3 / -6)

Slope (m) = -3/-6 = 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 intercept formula:

y – mx = b

y=4, m=1/2, x =7

y – mx = b

b= .5

The slope intercept form 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.

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:

$$x_2 = x_1 + \frac{-d}{\sqrt(1 + m^2)}$$
$$y_2 = y_1 + m \times \frac{-d}{\sqrt(1 + m^2)}$$

How to Solve the (Δ) Delta 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 = x₂ – x₁

The (Δ) delta of y can be determined using the formula:

Δy = y₂ – y₁

When Slope and 1 Point Are Known:

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 point slope calculator to perform instant calculations instead of sticking to these manual calculation steps!

FAQ’s (Slope, Line, Points, and more)

How do you calculate slope?

The slope of a line is something that characterizes the direction of the line. If you want to calculate slope, all you need to divide the different of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. Also, our simple slope calculator helps you to calculate slope immediately.

How do you calculate a 2% slope?

Slope as a Percentage:

Yes, slope 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 x 100 = an 8.3% slope.

Is slope the same thing as gradient?

In short, Yes! “Slope” is term that sometimes also referred to as a “Gradient”.

How do I find slope of 2x – 4y = 20?

You ought to re-work the equation until ‘y’ is isolated on one side. Very next, you ought to note the coefficient of the x term, that is said be as the slope. In this equation, you re-work the equation until you isolate y: y = x/2 – 5. The coefficient of x is said to be as 1/2, means the slope of the line is 1/2.

How do I find the slope of a line y=9?

For all the lines where ‘y’ equals a constant and there is no ‘x’, the slope is said to be as 0.

What is the slope of Y 4?

The line is horizontal; the slope is expressed as a 0. So, the slope is 0 and the y-intercept is -4.

What is a 1% slope in inches?

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 × 12 = 960 inches the rise should be 0.01 × 960 = 9.6 inches.

What is the slope of 1/4 inch per foot?

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

What is a 20% slope?

Slope percent = (8 feet / 40 feet) × 100 = 0.20 × 100 = 20%

The slope percent is 20%.

What is the slope of the line through (- 10 1 and 0 4)?

The slope of these points (-10, 1) and (-4, 0) is perpendicular to this line.

What is the slope of y =- 4x 3?

In this equation, the slope is expressed as −4 as this equation is in slope-intercept form that is y=mx+c , where m is the slope.

How do I use a protractor and trigonometry to find slope of a line?

The slope of a line is indicated a non-angular representation of the angle between the line and a horizontal line such as the x-axis. You ought to use a protractor to measure that angle, and very next, you ought to convert the angle to a decimal or a fraction using a trig table.

For instance:

If a protractor shows you that there is a 45° angle between the line and a horizontal line, a trig table is assists to tell you that the tangent of 45° is 1, which is said to be the line’s slope. Remember that most angles do not have such a simple tangent. For example, an angle of 30° has a tangent of 0.577. However, you could account that as the slope, or even convert the decimal to a fraction, but if we look at this case, it would be a rather unwieldy fraction (577/1000 or 72/125).

How do I find the slope of a function with 3 nonlinear points?

You are elaborating a curved line. It is said that each point on a curve has its own unique slope, remember that the curve or function as a whole doesn’t have a specific slope.

Does it matter which two points I choose?

No, it doesn’t matter at all since the line increases at a constant rate, the ratio of (y2-y1)/(x2-x1) will remain the same.

How do I find a slope with no points?

Simply, you ought to use a protractor and trigonometry!

Can I find the slope of -1?

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.

Takeaway:

Luckily, you come to know how to find slope. The amazing thing is that there is no need to remember these formulas, you just have to account the above calculator to  find the slope and distance between two points, slope & angle, x and y intercept, and slope intercept form for a given parameters