Slope
Slope measures steepness as rise over run.
About this topic
Slope measures how steep a line is and in which direction it leans. It is the ratio of vertical change to horizontal change, "rise over run", or (y₂ − y₁)/(x₂ − x₁). A positive slope climbs to the right, a negative slope falls, a horizontal line has slope zero, and a vertical line has undefined slope because its run is zero.
Slope is really a rate of change: how much the output changes for each one-unit step in the input. For the points (1, 2) and (4, 8) the rise is 6 and the run is 3, so the slope is 2, meaning y goes up two for every one step in x. The same value comes out no matter which two points on the line you choose, which is exactly what makes a line straight.
Slope appears everywhere: the grade of a road, the pitch of a roof, the speed on a distance-time graph, or the cost per item in a pricing plan. Builders use it to design wheelchair ramps with safe steepness.
Typical errors include subtracting in a different order on top and bottom, which flips the sign, and confusing zero slope with undefined slope. Picture a flat floor for zero and a wall for undefined.
Key ideas
- m = (y₂ − y₁)/(x₂ − x₁)
- Positive slopes rise, negative fall
- Horizontal lines have slope 0
Quick check
Use cases: where Slope helps
- Homework: review the key idea behind Slope before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Slope without notes.
- Visual learning: play with the interactive lab to see how Slope changes when you adjust its inputs.
- Teaching a friend: explain Slope in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Slope?
Slope measures steepness as rise over run.
What will I learn in Slope?
m = (y₂ − y₁)/(x₂ − x₁). Positive slopes rise, negative fall. Horizontal lines have slope 0.
Is Slope part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Slope lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Slope?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.