Unit 4 · Topic 1

Slope

Overview

Measure steepness as rise over run.

Topic 1 of 2~24 min
Next: Slope-Intercept FormAll units
Unit overview

The lesson

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).

Slope from two points

  1. 1Pick two points (x₁, y₁) and (x₂, y₂).
  2. 2Slope m = (y₂ − y₁) ÷ (x₂ − x₁).
Worked example

Find the slope through (1, 2) and (4, 8).

  1. 1Change in y: 8 − 2 = 6.
  2. 2Change in x: 4 − 1 = 3.
  3. 3Slope = 6 ÷ 3 = 2.

Why this matters

Measure steepness as rise over run.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.

Re-reading the question too quickly. Underline what you are solving for before you start calculating.

Key ideas from this lesson

  1. Rise over run
  2. Slope from two points
  3. Pick two points (x₁, y₁) and (x₂, y₂).
  4. Slope m = (y₂ − y₁) ÷ (x₂ − x₁).

Video walkthroughs

Khan Academy

Finding the Slope of a Line

Slope as change in y over change in x.

Watch on YouTube
Khan Academy

Slope from Two Points

Compute slope from a pair of ordered pairs.

Watch on YouTube
Khan Academy

Slope and y-Intercept from an Equation

Read slope and intercept directly from a linear equation.

Watch on YouTube
Khan Academy

Graphs of Linear Equations

Plot points to graph a line from its slope.

Watch on YouTube

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 yourself

Find the slope of the line through (0, 1) and (2, 5).

Step-by-step solution

  1. 1Change in y: 5 − 1 = 4.
  2. 2Change in x: 2 − 0 = 2.
  3. 3Slope = 4 ÷ 2 = 2.

Exercise 2

Try it yourself

Find the slope through (−1, 4) and (3, −4).

Step-by-step solution

  1. 1Change in y: −4 − 4 = −8.
  2. 2Change in x: 3 − (−1) = 4.
  3. 3Slope = −8 ÷ 4 = −2.

Exercise 3

Try it yourself

A line rises 6 units and runs 2 units to the right. What is its slope?

Step-by-step solution

  1. 1Rise = 6, run = 2.
  2. 2Slope = 6/2 = 3.
  3. 3The slope is 3.

Exercise 4

Try it yourself

What is the slope of a vertical line?

Step-by-step solution

  1. 1On a vertical line, all points share the same x-value.
  2. 2Change in x = 0, so rise/run divides by zero.
  3. 3Slope is undefined.

Exercise 5

Try it yourself

Line A has slope 3/4. Line B has slope −3/4. How are their directions related?

Step-by-step solution

  1. 1Slopes have the same magnitude but opposite signs.
  2. 2One line goes up left-to-right; the other goes down.
  3. 3They are opposite (negative reciprocal is for perpendicular, not here).

Re-read the lesson section if you get stuck, then try again without peeking at the solution.

Khan Academy

Slope

Open resource

Quick check

Answer all questions. Retake the quiz until you feel confident before moving on.

Slope

Question 1 of 4

Medium

Find the slope through (2, 3) and (6, 11).

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