The Pythagorean Theorem
9-12
1
Slope-Intercept Form
Lesson Details
Grade Level
9-12
Duration (minutes)
1
Summary
A Grade 9-12 math lesson teaching students how to identify the slope and y-intercept from an equation in slope-intercept form (y = mx + b), and how to write an equation given a slope and a point, with two fully worked examples.
Student Worksheet: Slope-Intercept Form
Teacher Note: Students can watch the video lesson above and answer the questions. Click the “Teacher Answer Key” dropdown below when you are ready to review the solutions!
Key Concepts:
• Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.
• Slope: Tells how the line changes; a positive slope means the line rises from left to right.
• Y-Intercept: The point where the line crosses the y-axis, written as (0, b).
• Writing an Equation: If you know the slope and a point on the line, substitute both into y = mx + b and solve for b.
Instructions: Read each question carefully and write your answer in the space provided.
- Question 1: In slope-intercept form y = mx + b, what do m and b each represent?
- Question 2: Identify the slope and y-intercept of y = 3x + 5.
- Question 3: What does a positive slope tell you about a line?
- Question 4: Write the equation of a line with a slope of 2 that passes through the point (1, 4). Show your steps.
- Question 5: In Question 4, why do you substitute the point’s x and y values into y = 2x + b before solving for b?
Click to reveal Teacher Answer Key
1. m is the slope, and b is the y-intercept.
2. Slope (m) = 3, y-intercept (b) = 5.
3. A positive slope means the line rises from left to right.
4. y = mx + b → y = 2x + b → 4 = 2(1) + b → 4 = 2 + b → b = 2. Final equation: y = 2x + 2.
5. Because the point (1, 4) must satisfy the equation of the line, so substituting its x and y values lets you solve for the unknown b.
Disclaimer: This worksheet was generated with AI assistance based on original video content. It is intended for educational reference only. Teachers are encouraged to review and adjust questions to fit their curriculum standards before classroom use.
🎯 Extension Activity: Identify the slope and y-intercept of y = -4x + 7. Then write the equation of a line with a slope of -1 that passes through the point (2, 3). Show every step.