Slope Formula

beginneralgebralinear equations

Calculates the steepness or inclination of a line

The Formula

m = (y₂ - y₁) / (x₂ - x₁)

Variables & Symbols

m

Slope (rate of change)

(x₁, y₁)

First point on the line

(x₂, y₂)

Second point on the line

When to Use This Formula

  • Finding the steepness of a line
  • Determining if lines are parallel or perpendicular
  • Writing equations of lines
  • Rate of change problems

Worked Examples

Example 1

Problem:

Find slope between (1, 2) and (4, 8)

Solution: m = 2

Step-by-Step:

1

Identify: (x₁,y₁) = (1,2), (x₂,y₂) = (4,8)

2

m = (8 - 2) / (4 - 1)

3

m = 6 / 3

4

m = 2

Common Mistakes to Avoid

  • Reversing the order (x difference in numerator)
  • Dividing by zero for vertical lines
  • Sign errors with negative coordinates

Real-World Applications

1

Road grade and incline calculations

2

Roof pitch in construction

3

Rate of change in economics

4

Physics - velocity and acceleration

Practice Problems

Problem 1: Slope of (0,0) and (3,6)

Show Answer

Answer: m = 2

Problem 2: Slope of (2,5) and (2,9)

Show Answer

Answer: undefined (vertical)

Related Formulas

point slope form

View Formula →

slope intercept form

View Formula →

parallel lines

View Formula →

perpendicular lines

View Formula →

Tags:

algebraslopelinear equationslines

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