Slope and Y Intercept Calculator

Slope and Y-Intercept Calculator

Enter the coordinates of two distinct points to calculate the slope (m) and y-intercept (b) of the line passing through them. The calculator will also provide the equation of the line in the form y = mx + b.

Understanding Slope and Y-Intercept

In mathematics, particularly in algebra and geometry, the slope and y-intercept are fundamental characteristics of a straight line. They provide crucial information about the line's orientation and position on a coordinate plane.

What is Slope (m)?

The slope, often denoted by 'm', measures the steepness and direction of a line. It represents the "rise over run" – how much the y-coordinate changes for a given change in the x-coordinate. A positive slope indicates an upward trend from left to right, a negative slope indicates a downward trend, a zero slope means the line is horizontal, and an undefined slope means the line is vertical.

The formula for calculating the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:

m = (y₂ – y₁) / (x₂ – x₁)

What is Y-Intercept (b)?

The y-intercept, often denoted by 'b', is the point where the line crosses the y-axis. At this point, the x-coordinate is always zero (0, b). It represents the initial value or starting point of a linear relationship when the independent variable (x) is zero.

Once the slope (m) is known, the y-intercept (b) can be calculated using one of the points (x₁, y₁) and the slope:

b = y₁ – m * x₁

The general equation of a straight line is given by:

y = mx + b

How to Use This Calculator

1. Enter the x and y coordinates for your first point (x₁, y₁) into the respective fields.
2. Enter the x and y coordinates for your second point (x₂, y₂) into the respective fields.
3. Click the "Calculate Slope & Y-Intercept" button.
4. The calculator will display the calculated slope, y-intercept, and the equation of the line.

Example Calculation

Let's say we have two points: Point 1 (2, 5) and Point 2 (6, 13).

Step 1: Calculate the Slope (m)

x₁ = 2, y₁ = 5

x₂ = 6, y₂ = 13

m = (13 – 5) / (6 – 2)

m = 8 / 4

m = 2

Step 2: Calculate the Y-Intercept (b)

Using Point 1 (2, 5) and m = 2:

b = y₁ – m * x₁

b = 5 – 2 * 2

b = 5 – 4

b = 1

Step 3: Formulate the Equation of the Line

With m = 2 and b = 1, the equation of the line is:

y = 2x + 1

This calculator automates these steps for any two given points.

Error:

Error:

Slope (m):

Y-intercept (b):

Equation of the Line:

Slope (m):

Y-intercept (b):

Equation of the Line: