The lesson
This lesson teaches Slope. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Rise over run
Slope tells how steep a line is. It is the change in y (rise) divided by the change in x (run).
When you study rise over run, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Slope from two points
When you study slope from two points, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
- 1Pick two points (x₁, y₁) and (x₂, y₂).
- 2Slope m = (y₂ − y₁) ÷ (x₂ − x₁).
Find the slope through (1, 2) and (4, 8).
- 1Change in y: 8 − 2 = 6.
- 2Change in x: 4 − 1 = 3.
- 3Slope = 6 ÷ 3 = 2.
Why this matters
Slope shows up constantly in measure steepness as rise over run. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- Rise over run
- Slope from two points
- Pick two points (x₁, y₁) and (x₂, y₂).
- Slope m = (y₂ − y₁) ÷ (x₂ − x₁).
Video walkthrough
Practice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfFind the slope of the line through (0, 1) and (2, 5).
Step-by-step solution
- 1Change in y: 5 − 1 = 4.
- 2Change in x: 2 − 0 = 2.
- 3Slope = 4 ÷ 2 = 2.
Exercise 2
Try it yourselfFind the slope through (−1, 4) and (3, −4).
Step-by-step solution
- 1Change in y: −4 − 4 = −8.
- 2Change in x: 3 − (−1) = 4.
- 3Slope = −8 ÷ 4 = −2.
Exercise 3
Try it yourselfA line rises 6 units and runs 2 units to the right. What is its slope?
Step-by-step solution
- 1Rise = 6, run = 2.
- 2Slope = 6/2 = 3.
- 3The slope is 3.
Exercise 4
Try it yourselfWhat is the slope of a vertical line?
Step-by-step solution
- 1On a vertical line, all points share the same x-value.
- 2Change in x = 0, so rise/run divides by zero.
- 3Slope is undefined.
Exercise 5
Try it yourselfLine A has slope 3/4. Line B has slope −3/4. How are their directions related?
Step-by-step solution
- 1Slopes have the same magnitude but opposite signs.
- 2One line goes up left-to-right; the other goes down.
- 3They are opposite (negative reciprocal is for perpendicular, not here).
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Slope
Question 1 of 4
Find the slope through (2, 3) and (6, 11).