Education Calculators ▶ Slope Calculator
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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.
So, let’s start with the simple definition of ‘slope definition.’
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.
There are four different types of slope that all are depending on the direction of the line. Read on!
Let’s digging deeper!
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.
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.
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.
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.
Slope (m) = ΔY/ΔX
In this slope equation;
M = slope
ΔY = (y₂ – y₁)
ΔX = (x₂ – x₁)
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:
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:
Input:
Output:
Once you entered all the above parameters, then simply hit the calculate button, the slope calculator for two points will generate:
Input:
Output:
Once done, then simply hit the calculate button, this slope intercept form calculator will provides you with:
Input:
Output:
Once you added all the above-parameters, hit the calculate button, this point slope calculator will generates:
Input:
Output:
Once you filled the all parameters, then simply hit the calculate button, this slope (m) calculator will generates:
Input:
Output:
Once you entered the line equation, then hit the calculate button, this slope of a line calculator will generates:
Thankfully, you come to know how to find the slope using the simple slope of a line formula.
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))
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(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).
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).
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;
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.
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 = x₂ – x₁
The (Δ) delta of y can be determined using the formula:
Δy = y₂ – y₁
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!
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.
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!
For instance:
“2” rise divided by “24” run = .083 x 100 = an 8.3% slope.
In short, Yes! “Slope” is term that sometimes also referred to as a “Gradient”.
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.
For all the lines where ‘y’ equals a constant and there is no ‘x’, the slope is said to be as 0.
The line is horizontal; the slope is expressed as a 0. So, the slope is 0 and the y-intercept is -4.
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.
1/4″ per foot pitch equals to 2% (percent), and remember that it is not expressed as 2 degrees.
Slope percent = (8 feet / 40 feet) × 100 = 0.20 × 100 = 20%
The slope percent is 20%.
The slope of these points (-10, 1) and (-4, 0) is perpendicular to this line.
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.
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).
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.
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.
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.
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
From Wikipedia, the free encyclopedia – what is the slope – Examples and Statistics of Slope
The Source of Mathplanet recently updated – Pre-Algebra / Graphing and functions / – how to find slope – The slope of a linear function
From the source of mathblog – An Introduction To Algebra – How To Calculate Slope – 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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