Slope Calculator and Point-Slope Form
Enter two points, (x₁, y₁) and (x₂, y₂). The calculator writes the line through them in slope-intercept form, y = mx + b, and shows the slope, the distance between the points and the angle from the first point to the second. Slope and distance are rounded to 4 decimal places, the angle to 2. It also writes the point-slope form, y − y₁ = m(x − x₁). If you already know a point and the slope, switch to Point and slope and you get both forms and the intercepts.
How to use the Slope Calculator
- Enter your numbers in the Slope Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The line formulas
Slope: m = (y₂ − y₁)/(x₂ − x₁) · · · Distance: d = √((x₂ − x₁)² + (y₂ − y₁)²) · · · Line: y − y₁ = m(x − x₁)
Slope is rise over run. Distance is the hypotenuse of a right triangle whose legs are the two differences. The calculator writes the line in slope-intercept form, y = mx + b, with b = y₁ − m·x₁. The angle is the direction from the first point to the second, measured from the positive x-axis, between −180° and 180°.
Worked example
Points (1, 2) and (5, 10): slope = (10 − 2)/(5 − 1) = 8/4 = 2. Distance = √(4² + 8²) = √80, which the calculator shows as 8.9443. The line is y = 2x + 0, so it passes through the origin, and the angle is 63.43°. Swap the two points and the slope and line stay the same, but the angle turns to −116.57°, because the direction now runs from (5, 10) back to (1, 2). The point-slope form from (1, 2) is y − 2 = 2(x − 1). For the point (−3, 2) and slope 2/3, Point and slope gives y − 2 = 0.6667(x + 3) and y = 0.6667x + 4. The line crosses the axes at (0, 4) and (−6, 0).
Frequently asked questions
What does negative slope mean?
The line goes downward from left to right. A slope of −2 means y decreases by 2 for every 1 unit x increases.
What is the slope of a vertical line?
It has none, because x₂ − x₁ is zero and you can't divide by zero. The calculator shows the slope as Undefined (vertical line) and writes the line as x = constant, such as x = 2 for the points (2, 1) and (2, 5).
What is point-slope form?
It is y − y₁ = m(x − x₁), where m is the slope and (x₁, y₁) is any point on the line. A negative coordinate turns the minus into a plus, so the point (−3, 2) with slope 4 gives y − 2 = 4(x + 3). Multiply it out and move y₁ across to get y = 4x + 14, the slope-intercept form. The calculator shows both forms.
Can I enter the slope as a fraction?
Yes, in Point and slope mode. Type 2/3 or -1/4 in the slope box. The calculator works with the full value and prints it rounded to 4 decimal places, so 2/3 shows as 0.6667.
How do I find a perpendicular line?
A line perpendicular to slope m has slope −1/m. So a line perpendicular to y = 2x + 3 has slope −1/2.