Slope Intercept Form Calculator
Find the equation of a line in y = mx + b format with step-by-step solutions
Calculate Slope-Intercept Form
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Visual Graph
Results
Slope-Intercept Form
Slope (m)
Y-Intercept (b)
X-Intercept
Standard Form
Step-by-Step Solution
Point 2: (1, 1)
b = 0 - 0.000000 = 0.000000
x = -0.000000 / 1.000000 = 0.000000
Example Problems
Example 1: From Two Points
Points: (1, 2) and (3, 8)
Example 2: From Slope and Intercept
Slope: -2, Y-intercept: 5
Example 3: From Point and Slope
Point: (2, -1), Slope: 0.5
Formula Reference
Slope-Intercept Form
y = mx + b
Slope Formula
m = (y₂ - y₁) / (x₂ - x₁)
X-Intercept
x = -b / m
Standard Form
Ax + By + C = 0
Line Properties
Slope (m)
Steepness and direction of the line
Y-Intercept (b)
Where the line crosses the y-axis
X-Intercept
Where the line crosses the x-axis
Parallel Lines
Same slope, different y-intercepts
Perpendicular Lines
Slopes are negative reciprocals
Understanding Slope-Intercept Form
What is Slope-Intercept Form?
The slope-intercept form is written as y = mx + b, where:
- •m is the slope (rise over run)
- •b is the y-intercept (where line crosses y-axis)
- •x and y are coordinates of any point on the line
Why Use This Form?
The slope-intercept form is the most intuitive way to understand a linear equation because it immediately shows you the two most important characteristics of a line: its steepness (slope) and where it starts on the y-axis (y-intercept).
Slope Interpretation
Positive Slope
Line rises from left to right. For every 1 unit increase in x, y increases by m units.
Negative Slope
Line falls from left to right. For every 1 unit increase in x, y decreases by |m| units.
Zero Slope
Horizontal line. y remains constant regardless of x value.
Undefined Slope
Vertical line. Cannot be expressed in slope-intercept form.
Real-World Applications
Business & Economics
Cost functions, revenue models, and linear relationships between variables like price and demand.
Physics & Engineering
Velocity (slope) in position vs time graphs, force relationships, and linear motion analysis.
Data Analysis
Linear regression, trend analysis, and predicting future values based on current data patterns.
Converting Between Forms
From Standard Form (Ax + By + C = 0)
Solve for y:
By = -Ax - C
y = (-A/B)x + (-C/B)
So m = -A/B and b = -C/B
From Point-Slope Form
y - y₁ = m(x - x₁)
y - y₁ = mx - mx₁
y = mx - mx₁ + y₁
So b = y₁ - mx₁