Equation
y = 2x
Slope (m)
2.0000
y-intercept (b)
0.0000
y = 2x
2
0
0
63.43°
m = (y₂ - y₁) / (x₂ - x₁)Calculates the slope (rate of change) of a line through two points. Positive slope goes up, negative goes down, zero is horizontal.
Where:
m= The slope of the line (rise over run)(x₁, y₁)= Coordinates of the first point(x₂, y₂)= Coordinates of the second pointy = mx + bThe standard form of a linear equation where m is the slope and b is the y-intercept. Every non-vertical line can be expressed this way.
Where:
m= Slope of the lineb= y-intercept (value of y when x = 0)x, y= Any point (x, y) on the linem⊥ = -1 / mThe slope of a line perpendicular to a line with slope m. Two perpendicular lines satisfy m₁ × m₂ = -1.
Where:
m= Slope of the original linem⊥= Slope of the perpendicular lineInputs
Result
m = (8-2)/(4-1) = 6/3 = 2. Then b = 2 - 2×1 = 0. The line passes through the origin with equation y = 2x.
Inputs
Result
m = (-1-5)/(3-0) = -6/3 = -2. Then b = 5 - (-2)×0 = 5. The line crosses the y-axis at 5 and x-axis at 2.5.
Inputs
Result
b = y₁ - m×x₁ = 7 - 3×2 = 7 - 6 = 1. The equation is y = 3x + 1. The perpendicular slope is -1/3.
Slope-intercept form y = mx + b is the most common way to write the equation of a line. The variable m represents the slope (how steep the line is) and b represents the y-intercept (where the line crosses the y-axis). Any non-vertical line can be written in this form.
| Equation | Slope (m) | y-intercept (b) |
|---|---|---|
| y = 2x + 3 | 2 | 3 |
| y = -x + 5 | -1 | 5 |
| y = 0.5x | 0.5 | 0 |
| y = 4 | 0 | 4 |
The slope formula is m = (y₂ - y₁) / (x₂ - x₁), which calculates rise over run. Subtract the y-coordinates and divide by the difference of the x-coordinates. A positive slope means the line goes up from left to right; negative means it goes down.
| Points | Rise / Run | Slope |
|---|---|---|
| (1,2) to (4,8) | 6 / 3 | 2 |
| (0,3) to (6,0) | -3 / 6 | -0.5 |
| (2,5) to (5,5) | 0 / 3 | 0 |
| (-1,4) to (3,0) | -4 / 4 | -1 |
Parallel lines have identical slopes (m₁ = m₂). Perpendicular lines have slopes that are negative reciprocals, meaning m₁ × m₂ = -1. For example, if one line has slope 2, a perpendicular line has slope -1/2. These relationships are fundamental in geometry.
| Original Slope | Parallel Slope | Perpendicular Slope |
|---|---|---|
| m = 2 | 2 | -0.5 |
| m = -3 | -3 | 0.333 |
| m = 1 | 1 | -1 |
| m = 0.25 | 0.25 | -4 |
The y-intercept is the value of b in y = mx + b (set x = 0). The x-intercept is found by setting y = 0 and solving: x = -b/m. For example, for y = 2x + 6, the y-intercept is 6 and the x-intercept is -6/2 = -3.
| Equation | y-intercept | x-intercept |
|---|---|---|
| y = 2x + 6 | (0, 6) | (-3, 0) |
| y = -x + 4 | (0, 4) | (4, 0) |
| y = 3x - 9 | (0, -9) | (3, 0) |
| y = 0.5x + 1 | (0, 1) | (-2, 0) |
The angle of inclination is the angle a line makes with the positive x-axis, calculated as θ = arctan(m). A slope of 1 gives 45°, slope of 0 gives 0°, and undefined slope (vertical) gives 90°. Negative slopes produce negative angles measured clockwise from the x-axis.
| Slope (m) | Angle (θ) | Direction |
|---|---|---|
| 0 | 0° | Horizontal |
| 1 | 45° | 45° diagonal up |
| -1 | -45° | 45° diagonal down |
| Undefined | 90° | Vertical |
The slope-intercept form y = mx + b is the most intuitive way to express a linear equation. The slope m tells you how much y changes for each unit increase in x (rise over run), while the y-intercept b tells you where the line crosses the y-axis.
Finding the equation from two points is a two-step process: first calculate the slope m = (y₂-y₁)/(x₂-x₁), then solve for b using b = y₁ - m·x₁. If you already know the slope and one point, you only need the second step.
Our slope-intercept calculator supports both input modes, computes the complete line equation, identifies x and y intercepts, calculates the angle of inclination, and finds parallel and perpendicular slopes. Every result includes a step-by-step derivation.
Last Updated: Mar 11, 2026
This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.