Slope
Rate of change: rise over run.
Key idea
Rate of change: rise over run.
In depth
Slope measures steepness: m = rise/run = (y₂ − y₁)/(x₂ − x₁). It is the rate of change of y per unit of x. Positive slope rises, negative falls, zero is horizontal, and vertical lines have undefined slope.
Worked example
Through (1, 2) and (4, 8): m = (8−2)/(4−1) = 2.
Formula
Real-world uses
- Measuring road gradients and roof pitch
- Calculating the rate of a rising price or falling water level
Common mistake
Mixing the order of subtraction in numerator and denominator; keep both the same direction.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Slope?
Rate of change: rise over run. It is a topic at the intermediate level in Algebra.
What is the formula for Slope?
The key formula is m = (y₂ − y₁)/(x₂ − x₁).
Where is Slope used in real life?
Real-world examples: Measuring road gradients and roof pitch; Calculating the rate of a rising price or falling water level.
What should I learn before Slope?
Make sure you are comfortable with Coordinate Plane, the previous topic in Algebra.
What is a common mistake with Slope?
Mixing the order of subtraction in numerator and denominator; keep both the same direction.
How can I practise Slope?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Slope?
Move on to Slope-Intercept Form next.
Related intermediate topics in Algebra
- Multi-Step Equations – Distribute, combine like terms, move variables to one side.
- Variables on Both Sides – Collect variable terms on one side first.
- Literal Equations – Rearrange formulas to solve for a chosen variable.
- Identity and No-Solution Equations – Some equations are always true or never true.
- Linear Inequalities – Solve like equations but reverse the sign when multiplying by a negative.
- Compound Inequalities – Combine two inequalities using “and” or “or”.