Slope & Intercept Calculator - Linear Equations
Calculate slope, y-intercept, and x-intercept from two points or an equation. Get the slope-intercept form with step-by-step solutions.
Input Method
Results
What is a Slope & Intercept Calculator?
A Slope & Intercept Calculator is a mathematical tool that determines the key properties of a linear equation, including the slope, y-intercept, and x-intercept. It can work from two points or from an equation in standard form.
This calculator provides:
- Slope (m) - The rate of change of the line
- Y-Intercept (b) - Where the line crosses the y-axis
- X-Intercept - Where the line crosses the x-axis
- Slope-Intercept Form - The equation y = mx + b
For distance and midpoint calculations, try our Distance, Midpoint & Slope Calculator with comprehensive geometry tools.
To visualize linear functions, check our Linear Function Graphing Calculator for interactive graphs.
To solve systems of equations, use our Simultaneous Equations Solver for 2×2 and 3×3 systems.
How the Calculator Works
From Two Points (x₁, y₁) and (x₂, y₂):
Y-Intercept: b = y₁ - m × x₁
X-Intercept: x = -b / m
From Equation (ax + by = c):
Y-Intercept: b = c / b
X-Intercept: x = c / a
The final equation is expressed in slope-intercept form: y = mx + b
Understanding Slope and Intercepts
Slope (m)
Represents the steepness and direction of the line. Positive slopes rise, negative slopes fall.
Y-Intercept (b)
The y-coordinate where the line crosses the y-axis (when x = 0).
X-Intercept
The x-coordinate where the line crosses the x-axis (when y = 0).
Special Cases
Vertical lines have undefined slope; horizontal lines have slope = 0.
How to Use This Calculator
Select Mode
Choose two points or equation
Enter Values
Input coordinates or coefficients
Click Calculate
Get slope and intercepts instantly
Review Steps
See detailed solution process
Benefits of Using This Calculator
- • Dual Input Methods: Calculate from two points or from an equation in standard form.
- • Complete Analysis: Get slope, both intercepts, and the slope-intercept equation.
- • Step-by-Step Solutions: Understand the calculation process with detailed explanations.
- • Educational Tool: Perfect for students learning linear equations and coordinate geometry.
Understanding Line Types
Positive Slope
Line rises from left to right. As x increases, y increases.
Negative Slope
Line falls from left to right. As x increases, y decreases.
Zero Slope
Horizontal line. y-value remains constant regardless of x.
Undefined Slope
Vertical line. x-value remains constant, cannot be written as y = mx + b.
Frequently Asked Questions (FAQ)
Q: What is the slope-intercept form of a linear equation?
A: The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This form makes it easy to identify the rate of change and where the line crosses the y-axis.
Q: How do you calculate slope from two points?
A: The slope m is calculated using the formula m = (y₂ - y₁) / (x₂ - x₁), which represents the change in y divided by the change in x between two points.
Q: What is the difference between x-intercept and y-intercept?
A: The y-intercept is where the line crosses the y-axis (when x = 0), while the x-intercept is where the line crosses the x-axis (when y = 0).
Q: Can a line have no x-intercept?
A: Yes, horizontal lines (except y = 0) have no x-intercept because they never cross the x-axis. These lines have a slope of 0.
Q: How do you convert standard form to slope-intercept form?
A: To convert ax + by = c to slope-intercept form, solve for y: y = (-a/b)x + (c/b). The slope is -a/b and the y-intercept is c/b.