MathematicsChapter 8: Geometry of Straight Lines
Families
y = 2x + k is all parallels of slope 2.
Learning objectives
- Define and explain families.
- Apply families to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
y = 2x + k is all parallels of slope 2. y - 3 = m(x-1) is all lines through (1,3). The pair of axes is a special family. A question 'member of the family that...' means substitute the condition to find the parameter.
Formula
y = 2x + k is all parallels of slope 2. y -
Where / symbols
- Families
- y = 2x + k is all parallels of slope 2. y - 3 = m(x-1) is all lines through (1,3). The pair of axes is a special family. A question 'member of the family that...' means substitute the condition to find the parameter.
Relationship
- tan theta = |m2-m11+m1 m2|
Overview
Learn the idea, then use it:
Core Understanding
y = 2x + k is all parallels of slope 2. y - 3 = m(x-1) is all lines through (1,3). The pair of axes is a special family. A question 'member of the family that...' means substitute the condition to find the parameter.
Examples k slides a parallel · m rotates through a point · tan theta = |(m2-m1)/(1+m1 m2)| · FAMILIES: y = 2x + k is all parallels of slope 2. y - 3 = m(x-1) is all lines through (1,3). The pair of axes is a special family.
Exam Application
State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.
Examples Define first · Show the rule or evidence · Check units, labels, and conclusion
WHAT — FAMILIES
y = 2x + k is all parallels of slope 2. y - 3 = m(x-1) is all lines through (1,3). The pair of axes is a special family. A question 'member of the family that...' means substitute the condition to find the parameter.
HOW — Use the idea
Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.
In simple words
Do not merge families with a neighbouring idea that uses a different definition, rule, or method.
Key points
- k slides a parallel
- m rotates through a point
- tan theta = |m2-m11+m1 m2|
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Families
Sticky Notes · Quick Revision
Core Idea
- y = 2x + k is all parallels of slope 2.
Key Points
- k slides a parallel
- m rotates through a point
- tan theta = |m2-m11+m1 m2|
Simple Check
- Explain families in your own words and connect it to one chapter example.
How to Answer
- Define the idea, show the main rule or evidence, apply it, and check the final statement.
Common Mistake
- Do not merge families with a neighbouring idea that uses a different definition, rule, or method.
FBISE Exam Tip
- Use the exact term, show working where needed, and include units or labelled evidence.
60-second revision
- y = 2x + k is all parallels of slope 2.
- k slides a parallel
- m rotates through a point
- tan theta = |m2-m11+m1 m2|
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