There are two ways to use it. [From two points] Enter the coordinates of point 1 and point 2 to get the slope, the distance, the angle and the equation of the line. [From one point and a distance] Leave point 2 blank and enter the distance d and the slope m (or the angle θ) to get the coordinates of the point you reach from point 1.
Coordinates, distance and slope can be decimals or negative numbers. When point 2 (X2 and Y2) is filled in, the distance d, slope m and angle θ fields are not used. If you enter both the slope m and the angle θ, the slope m is used.
Result and graph
Enter the coordinates of two points in the fields on the left and press "Calculate". The result will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and graphs
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter the coordinates of two points and get the slope \(m\) of the line (the rate of change of a linear function) on the spot
- Along with the slope, it also finds the distance between the two points, the angle of inclination \(\theta\), the equation of the line \(y = mx + b\), the y-intercept and the x-intercept
- It also works the other way: from one point, a distance to move and a slope (or an angle), it finds the coordinates of the point you reach
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
The slope can be calculated only when the two points have different x-coordinates. A line through two points with the same x-coordinate (a vertical line) has an undefined slope, so "Undefined" is shown. The angle θ is measured counterclockwise from the positive x-axis and shown from 0° up to (but not including) 360°.
What is this calculation used for?
Checking whether a wheelchair ramp meets the rules (building and accessibility)
Under the ADA (Americans with Disabilities Act) standards, a wheelchair ramp can have a slope of at most 1:12 (1 up for every 12 across, a slope of about 0.083). Asking "can I build a 30-foot ramp to a porch that is 30 inches high?" is a slope calculation: \(30 \div 360 = \dfrac{1}{12}\) (30 feet = 360 inches), so it just meets the rule. As an angle, that is about 4.8°.
When remodeling a home or designing a building, you can check with numbers whether a ramp is safe to use.
Reading a "10% grade" road sign (driving and cycling)
A "10%" on a steep-grade sign says "it rises 10 ft for every 100 ft across", a slope of 0.1. As an angle, that is \(\arctan 0.1 \approx 5.7°\). Surprisingly few people know that 10% is not 10°.
Once you can read this, you can judge how steep a hill is in advance, when choosing a gear in a car or planning a bike or running route.
Finding the angle of a roof from its pitch (building and DIY)
In the US, the steepness of a roof is given as a pitch such as "4/12" (it rises 4 inches for every 12 inches across, a slope of 1/3). As an angle, that is \(\arctan \dfrac{4}{12} \approx 18.4°\).
Each roofing material can only be used within a certain range of pitches, so roofers and designers use this conversion every day. It also helps when you build a shed roof yourself.
Estimating how steep a hiking trail is and how far you really walk (hiking and maps)
If a trail climbs 1,000 ft over a horizontal distance of 1 mile (5,280 ft) on the map, its average slope is \(1000 \div 5280 \approx 0.19\) (an angle of about 10.7°), and by the Pythagorean theorem the distance you actually walk on the slope is \(\sqrt{5280^2 + 1000^2} \approx 5374\) ft.
Knowing with numbers that "the real distance is longer than on the map, and the slope decides how tiring it is" makes your hiking plans safer.
Reading how fast data changes from the slope (work and reading graphs)
If monthly sales grew from $40,000 in April to $58,000 in July, the slope is \((58{,}000 - 40{,}000) \div (7 - 4) = 6{,}000\) dollars per month, which reads as "growing by $6,000 a month on average".
The slope of a line graph is the pace of change itself. Finding how fast something changes from its values at two times, whether sales, body weight or temperature, is the same calculation as the slope formula on this page.
Formulas and graphs
Slope of a line \(m\) (rate of change)
Graph
Standard notation
(the usual math form)
\(m\)
\(=\)
\(y_2 - y_1\)
\(\div\)
\(x_2 - x_1\)
In words
(symbols replaced with words)
③
slope of the line \(m\)
\(=\)
①
change in y (rise) \(\Delta y = y_2 - y_1\)
\(\div\)
②
change in x (run) \(\Delta x = x_2 - x_1\)
The formula in words
①
Take the
change in y, \(\Delta y\) (how far it goes up or down)
②
divide it by the
change in x, \(\Delta x\) (how far it goes across)
③
and you get the
slope of the line \(m\)
Quick example
The slope of the line through the points (3, 4) and (6, 8) is
slope \(m\)
\(=\)
change in y (8 − 4 = 4)
\(\div\)
change in x (6 − 3 = 3)
\(m = \frac{8 - 4}{6 - 3} = \frac{4}{3} \approx 1.333\)
Key idea
The slope tells you "how much the line goes up or down for every 1 it goes across". It is often called "rise over run", and it is the same as the rate of change of a linear function from Grade 8 math. A positive slope rises from left to right, a negative slope falls from left to right, and a slope of 0 is a horizontal line.
Subtract in the same order on the top and the bottom (if you subtract point 1 from point 2, do it in both). If you mix the order, the sign comes out reversed. When the change in x is 0 (a vertical line), you would be dividing by 0, so the slope is undefined.
Distance between two points \(d\)
Graph
Standard notation
(the usual math form)
\(d\)
\(=\)
\(\sqrt{\Delta x^2 + \Delta y^2}\)
In words
(symbols replaced with words)
②
distance between the points \(d\)
\(=\)
①
square root of the sum of the squared changes \(\Delta x^2 + \Delta y^2\)
The formula in words
①
Take the
square root of the sum of the squared changes, \(\Delta x^2 + \Delta y^2\)
(square the change across and the change up, add them, and take the square root)
②
and you get the
distance between the points \(d\)
Quick example
The distance between the points (1, 1) and (4, 5) (Δx = 3, Δy = 4) is
distance \(d\)
\(=\)
square root of the sum of squares (3² + 4² = 25)
\(d = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\)
Key idea
This is just the Pythagorean theorem. Picture a right triangle whose two legs are the change across, \(\Delta x\), and the change up, \(\Delta y\). The segment joining the two points is its hypotenuse. Even if a change is negative, squaring makes it positive, so the formula works no matter where the points are.
Angle of inclination \(\theta\) (the angle of the line)
Graph
Standard notation
(the usual math form)
\(\theta\)
\(=\)
\(\arctan m\)
In words
(symbols replaced with words)
②
angle of inclination \(\theta\)
\(=\)
①
arctangent of the slope \(m\) (the angle found back from tan)
The formula in words
①
Take the
arctangent of the slope \(m\)
(find the angle whose tan is m)
②
and you get the
angle of inclination \(\theta\)
Quick example
The angle between the x-axis and a line with slope 1 (it rises 1 for every 1 to the right) is
angle of inclination \(\theta\)
\(=\)
arctangent of the slope (1)
\(\theta = \arctan 1 = 45^{\circ}\)
Key idea
The slope and the angle are linked by \(m = \tan\theta\). The arctangent (\(\arctan\), shown as tan⁻¹ on a scientific calculator) goes the other way, finding the angle from the slope. \(\arctan\) returns angles from −90° to 90°, so when the slope is negative (the line falls from left to right), the result is a negative angle. This calculator adds 360° to negative angles so that they are shown from 0° up to 360° (example: −63.4° → 296.6°). The angle of a vertical line is 90°.
When you work from two points, the angle is measured in the direction "from point 1 toward point 2", so if you enter the same two points in the opposite order, the angle points the opposite way (it differs by 180°).
Equation of a line \(y = mx + b\) (slope-intercept form)
Graph
Standard notation
(the usual math form)
\(y\)
\(=\)
\(m\)
\(\times\)
\(x\)
\(+\)
\(b\)
In words
(symbols replaced with words)
④
y-coordinate of a point on the line \(y\)
\(=\)
②
slope \(m\)
\(\times\)
①
x-coordinate \(x\)
\(+\)
③
y-intercept \(b\)
The formula in words
①
Take the
x-coordinate \(x\)
②
multiply it by the
slope \(m\)
③
add the
y-intercept \(b\)
④
and you get the
y-coordinate of the point on the line \(y\)
Quick example
The equation of the line with slope −2 through the point (1, 5) (the y-intercept is b = 5 − (−2) × 1 = 7) is
y-coordinate \(y\)
\(=\)
slope (−2)
\(\times\)
x-coordinate \(x\)
\(+\)
y-intercept (7)
\(b = y_1 - m x_1 = 5 - (-2) \times 1 = 7\)
\(y = -2x + 7\)
Key idea
Once you know the slope \(m\) and one point \((x_1, y_1)\) on the line, there is exactly one line. The y-intercept \(b\) comes from solving "the equation at that point", \(y_1 = m x_1 + b\), for \(b\): \(b = y_1 - m x_1\).
The y-intercept is the height where the graph crosses the y-axis (\(y\) when \(x = 0\)), and the x-intercept is where the graph crosses the x-axis (\(x\) when \(y = 0\)). The x-intercept is \(-b \div m\) (a horizontal line, \(m = 0\), has no x-intercept, unless it is the x-axis itself).
The point a distance \(d\) away from one point (given the slope \(m\))
Graph
Standard notation
(the usual math form)
\(\Delta x\)
\(=\)
\(d\)
\(\div\)
\(\sqrt{1 + m^2}\)
\(\Delta y\)
\(=\)
\(m\)
\(\times\)
\(\Delta x\)
In words
(symbols replaced with words)
③
change in x \(\Delta x\)
\(=\)
①
distance to move \(d\)
\(\div\)
②
square root of \(1 + m^2\)
⑥
change in y \(\Delta y\)
\(=\)
④
slope \(m\)
\(\times\)
⑤
change in x \(\Delta x\)
The formula in words
①
Take the
distance to move \(d\)
②
divide it by the
square root of \(1 + m^2\)
③
and you get the
change in x \(\Delta x\)
④
Next, multiply the
slope \(m\)
⑤
by the
change in x \(\Delta x\)
⑥
and you get the
change in y \(\Delta y\)
(so the point you reach is \((x_1 + \Delta x,\ y_1 + \Delta y)\))
Quick example
Starting at the point (1, 1) and moving a distance of 5 to the right along a line with slope 0.75, you reach
change in x \(\Delta x\)
\(=\)
distance to move (5)
\(\div\)
\(\sqrt{1 + 0.75^2}\) (= 1.25)
\(\Delta x = 5 \div \sqrt{1 + 0.75^2} = 5 \div 1.25 = 4\)
\(\Delta y = 0.75 \times 4 = 3\)
\((x_2,\ y_2) = (1 + 4,\ 1 + 3) = (5,\ 4)\)
Key idea
Why divide by \(\sqrt{1 + m^2}\)? Along a line with slope \(m\), going 1 across takes you \(m\) up, so by the Pythagorean theorem the length you actually travel is \(\sqrt{1 + m^2}\). In other words, "for every 1 across, you travel \(\sqrt{1 + m^2}\) along the line", so dividing the distance \(d\) by \(\sqrt{1 + m^2}\) gives the change across.
You can move in two directions, "to the right" (\(\Delta x\) positive) and "to the left" (negative), so this calculator shows both solutions. If you give an angle \(\theta\) instead of a slope, the angle also fixes the direction, so there is only one solution: \(\Delta x = d\cos\theta\), \(\Delta y = d\sin\theta\).
The slope of a line is "change in y ÷ change in x" (rise over run), the distance between two points comes from the Pythagorean theorem, and the angle comes from the arctangent. With these three tools, you can work out everything about a line from the coordinates of two points. You can also go the other way and find the point you reach from one point, a distance and a slope.
Symbols and terms
Symbols
| \(m\) | m | The slope of the line: how much it goes up or down for every 1 across. A positive slope rises from left to right; a negative slope falls. US schools use \(m\) for slope. |
| \((x_1, y_1)\), \((x_2, y_2)\) | x sub 1, y sub 1 | The coordinates of the two points. \(x\) is the horizontal position and \(y\) the vertical position; the small number at the lower right (the subscript) tells "the first point" from "the second point". |
| \(\Delta x\), \(\Delta y\) | delta x, delta y | The change (how much a value changed). \(\Delta\) (delta) is the Greek letter for "change": \(\Delta x = x_2 - x_1\) (the run) and \(\Delta y = y_2 - y_1\) (the rise). |
| \(d\) | d | The distance between the two points, from the first letter of "distance". |
| \(\theta\) | theta | A Greek letter often used for angles. On this page, it is the angle between the line and the x-axis (the angle of inclination). |
| \(b\) | b | The y-intercept: the height where the line crosses the y-axis (the value of \(y\) when \(x = 0\)). |
| \(\tan\) | tangent | A trigonometric ratio: "opposite ÷ adjacent", or "up ÷ across", for an angle. The slope of a line is linked to its angle by \(m = \tan\theta\). |
| \(\arctan\) | arctangent | The inverse of tangent: it finds "the angle whose tan is that number". On a scientific calculator it is shown as tan⁻¹. |
Terms
| slope | A number that shows how steep a line is: how much \(y\) increases when \(x\) increases by 1 ("rise over run"). The larger it is, the steeper the line. The grade of a road and the pitch of a roof use the same idea. |
| rate of change | (change in y) ÷ (change in x). It is taught with linear functions in Grade 8, and for a linear function it is exactly the same as the slope of the line. |
| linear function | A function of the form \(y = mx + b\). Its graph is a straight line, with slope \(m\) and y-intercept \(b\) (US schools write \(y = mx + b\); some other countries write \(y = ax + b\)). |
| intercept | Where a graph crosses an axis. The height where it crosses the y-axis is the y-intercept (\(y\) when \(x = 0\)), and where it crosses the x-axis is the x-intercept (\(x\) when \(y = 0\)). |
| angle of inclination | The angle a line makes with the x-axis (the horizontal). It is linked to the slope by \(m = \tan\theta\). |
| grade (pitch) | Everyday names for the steepness of a road, ramp or roof. A "10% grade" road sign says "it rises 10 ft for every 100 ft across", which is a slope of 0.1. Roof pitch is given as rise per 12 inches of run, such as 4/12. |
| coordinates | A pair of numbers (horizontal position, vertical position) that gives the location of a point. The point (3, 4) is "3 to the right and 4 up from the origin". Taught in Grade 6. |
| vertical line | A line perpendicular to the x-axis (going straight up). The change in x is 0, so the slope formula would divide by 0, and the slope is undefined. Its equation is not of the form \(y = mx + b\) but \(x = \text{constant}\). |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
If you get stuck, going back over these topics is the quickest way forward.
| The coordinate plane (Grades 5–6) |
|
| Adding and subtracting integers (Grades 6–7) |
|
| Linear functions and rate of change (Grade 8) |
|
| The Pythagorean theorem (Grade 8) |
|
| The tangent ratio (Geometry) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the slope m
| Point 1 x-coordinate x₁ | 3 |
| Point 1 y-coordinate y₁ | 4 |
| Point 2 x-coordinate x₂ | 6 |
| Point 2 y-coordinate y₂ | 8 |
| Slope m | =(B4-B2)/(B3-B1) |
Table to find the distance d between two points
| Point 1 x-coordinate x₁ | 3 |
| Point 1 y-coordinate y₁ | 4 |
| Point 2 x-coordinate x₂ | 6 |
| Point 2 y-coordinate y₂ | 8 |
| Distance between the points d | =SQRT((B3-B1)^2+(B4-B2)^2) |
Table to find the angle of inclination θ
| Point 1 x-coordinate x₁ | 3 |
| Point 1 y-coordinate y₁ | 4 |
| Point 2 x-coordinate x₂ | 6 |
| Point 2 y-coordinate y₂ | 8 |
| Angle of inclination θ (degrees) | =DEGREES(ATAN2(B3-B1,B4-B2)) |
Table to find the y-intercept and x-intercept
| x-coordinate of a point on the line x₁ | 1 |
| y-coordinate of a point on the line y₁ | 5 |
| Slope m | -2 |
| y-intercept b | =B2-B3*B1 |
| x-intercept | =-B4/B3 |
Table to find the point a distance d away from one point
| Point 1 x-coordinate x₁ | 1 |
| Point 1 y-coordinate y₁ | 1 |
| Distance to move d | 5 |
| Slope m | 0.75 |
| Change in x Δx | =B3/SQRT(1+B4^2) |
| Change in y Δy | =B4*B5 |
| x-coordinate reached x₂ | =B1+B5 |
| y-coordinate reached y₂ | =B2+B6 |
After pasting, the upper rows are your inputs and the formulas in the lower rows are calculated automatically.
"SQRT(…)" is the square root, "^2" squares a number, "DEGREES(…)" converts radians to degrees, and "ATAN2(change across, change up)" finds the angle from the changes in the two directions.
The first table gives a slope of about 1.333, the second a distance of 5, and the third an angle of about 53.13°. ATAN2 in the third table returns negative angles (from −180° to 180°), so for a line that falls from left to right, add 360 if you want the angle from 0 to 360°.
The fifth table finds the solution that goes to the right (the point (5, 4) in the example). For the solution that goes to the left, put a minus sign at the start of the Δx formula (=-B3/SQRT(1+B4^2)).
"SQRT(…)" is the square root, "^2" squares a number, "DEGREES(…)" converts radians to degrees, and "ATAN2(change across, change up)" finds the angle from the changes in the two directions.
The first table gives a slope of about 1.333, the second a distance of 5, and the third an angle of about 53.13°. ATAN2 in the third table returns negative angles (from −180° to 180°), so for a line that falls from left to right, add 360 if you want the angle from 0 to 360°.
The fifth table finds the solution that goes to the right (the point (5, 4) in the example). For the solution that goes to the left, put a minus sign at the start of the Δx formula (=-B3/SQRT(1+B4^2)).
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the slope m
| Point 1 x-coordinate x₁ | 3 |
| Point 1 y-coordinate y₁ | 4 |
| Point 2 x-coordinate x₂ | 6 |
| Point 2 y-coordinate y₂ | 8 |
| Slope m | =(B4-B2)/(B3-B1) |
Table to find the distance d between two points
| Point 1 x-coordinate x₁ | 3 |
| Point 1 y-coordinate y₁ | 4 |
| Point 2 x-coordinate x₂ | 6 |
| Point 2 y-coordinate y₂ | 8 |
| Distance between the points d | =SQRT((B3-B1)^2+(B4-B2)^2) |
Table to find the angle of inclination θ
| Point 1 x-coordinate x₁ | 3 |
| Point 1 y-coordinate y₁ | 4 |
| Point 2 x-coordinate x₂ | 6 |
| Point 2 y-coordinate y₂ | 8 |
| Angle of inclination θ (degrees) | =DEGREES(ATAN2(B3-B1,B4-B2)) |
Table to find the y-intercept and x-intercept
| x-coordinate of a point on the line x₁ | 1 |
| y-coordinate of a point on the line y₁ | 5 |
| Slope m | -2 |
| y-intercept b | =B2-B3*B1 |
| x-intercept | =-B4/B3 |
Table to find the point a distance d away from one point
| Point 1 x-coordinate x₁ | 1 |
| Point 1 y-coordinate y₁ | 1 |
| Distance to move d | 5 |
| Slope m | 0.75 |
| Change in x Δx | =B3/SQRT(1+B4^2) |
| Change in y Δy | =B4*B5 |
| x-coordinate reached x₂ | =B1+B5 |
| y-coordinate reached y₂ | =B2+B6 |
The same formulas as in Excel (SQRT, DEGREES, ATAN2 and ^2) work as is in Google Sheets. Copy the whole table, paste it into cell A1, and replace the input numbers with your own coordinates.
How to calculate it in Python
import math
x1, y1 = 3.0, 4.0 # coordinates of point 1
x2, y2 = 6.0, 8.0 # coordinates of point 2
delta_x = x2 - x1 # change in x (run)
delta_y = y2 - y1 # change in y (rise)
slope = delta_y / delta_x # slope m (if delta_x is 0, the line is vertical and this fails)
distance = math.hypot(delta_x, delta_y) # distance between the points (same as √(Δx²+Δy²))
angle = math.degrees(math.atan2(delta_y, delta_x)) % 360 # angle (0 to 360°)
y_intercept = y1 - slope * x1 # y-intercept b
print(f"Slope m: {slope}")
print(f"Distance d: {distance}")
print(f"Angle θ: {angle}")
print(f"Equation of the line: y = {slope}x + {y_intercept}")
# The other way: the point reached by moving a distance d from point (x1, y1) along the slope
d = 5.0
dx = d / math.sqrt(1 + slope ** 2) # solution going right (going left is -dx)
dy = slope * dx
print(f"Point reached: ({x1 + dx}, {y1 + dy})")
Runs with the standard library only. math.hypot is the square root of the sum of squares, and math.atan2 is the arctangent (a function that finds the angle from the changes across and up). Change the coordinates at the top and run it.
How to write it in LaTeX and other math languages (copy and paste)
Slope of a line \(m\) (rate of change)
m = (y₂ − y₁) ÷ (x₂ − x₁)
m = \frac{y_2 - y_1}{x_2 - x_1}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>m</mi>
<mo>=</mo>
<mfrac>
<mrow><msub><mi>y</mi><mn>2</mn></msub><mo>−</mo><msub><mi>y</mi><mn>1</mn></msub></mrow>
<mrow><msub><mi>x</mi><mn>2</mn></msub><mo>−</mo><msub><mi>x</mi><mn>1</mn></msub></mrow>
</mfrac>
</mrow>
</math>
m = (y_2 - y_1)/(x_2 - x_1)
(y2 - y1)/(x2 - x1)
m := (y2 - y1)/(x2 - x1);
m = (y2 - y1)/(x2 - x1);
m = (y_2 - y_1)/(x_2 - x_1)
Distance between two points \(d\)
d = √(Δx² + Δy²)
d = \sqrt{\Delta x^2 + \Delta y^2}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>d</mi>
<mo>=</mo>
<msqrt>
<mrow>
<msup><mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow><mn>2</mn></msup>
<mo>+</mo>
<msup><mrow><mi mathvariant="normal">Δ</mi><mi>y</mi></mrow><mn>2</mn></msup>
</mrow>
</msqrt>
</mrow>
</math>
d = sqrt((Delta x)^2 + (Delta y)^2)
Sqrt[dx^2 + dy^2]
d := sqrt(dx^2 + dy^2);
d = sqrt(dx^2 + dy^2);
d = √(Δx^2 + Δy^2)
Angle of inclination \(\theta\) (the angle of the line)
θ = arctan(m)
\theta = \arctan m
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>θ</mi>
<mo>=</mo>
<mi>arctan</mi>
<mo>⁡</mo>
<mi>m</mi>
</mrow>
</math>
theta = arctan(m)
ArcTan[m]
theta := arctan(m);
theta = atan(m);
θ = arctan(m)
Equation of a line \(y = mx + b\) (slope-intercept form)
y = mx + b (b = y₁ − m·x₁)
y = mx + b, \quad b = y_1 - m x_1
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>y</mi>
<mo>=</mo>
<mi>m</mi><mi>x</mi>
<mo>+</mo>
<mi>b</mi>
<mo>,</mo>
<mi>b</mi>
<mo>=</mo>
<msub><mi>y</mi><mn>1</mn></msub>
<mo>−</mo>
<mi>m</mi><msub><mi>x</mi><mn>1</mn></msub>
</mrow>
</math>
y = m x + b, b = y_1 - m x_1
b = y1 - m*x1; y = m*x + b
b := y1 - m*x1; y := m*x + b;
b = y1 - m*x1; y = m*x + b;
y = mx + b, b = y_1 - mx_1
The point a distance \(d\) away from one point (given the slope \(m\))
Δx = ±d ÷ √(1 + m²), Δy = m·Δx
\Delta x = \pm\frac{d}{\sqrt{1 + m^2}}, \quad \Delta y = m\,\Delta x
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow>
<mo>=</mo>
<mo>±</mo>
<mfrac>
<mi>d</mi>
<msqrt><mrow><mn>1</mn><mo>+</mo><msup><mi>m</mi><mn>2</mn></msup></mrow></msqrt>
</mfrac>
<mo>,</mo>
<mrow><mi mathvariant="normal">Δ</mi><mi>y</mi></mrow>
<mo>=</mo>
<mi>m</mi>
<mrow><mi mathvariant="normal">Δ</mi><mi>x</mi></mrow>
</mrow>
</math>
Delta x = +-d/sqrt(1 + m^2), Delta y = m Delta x
dx = d/Sqrt[1 + m^2]; dy = m*dx
dx := d/sqrt(1 + m^2); dy := m*dx;
dx = d/sqrt(1 + m^2); dy = m*dx;
Δx = ±d/√(1 + m^2), Δy = mΔx
How to have ChatGPT do the calculation
You are a math calculation assistant. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). For the two points (3, 4) and (6, 8) on the coordinate plane, find each of the following: 1. The slope m of the line through the two points 2. The distance d between the two points 3. The angle θ (in degrees) between the line and the x-axis 4. The equation of the line y = mx + b (also show the value of the y-intercept b) Show the formulas you used and the numbers from the execution result.
How to Use
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1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
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3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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