MathematicsChapter 6: Analytical Geometry
Family and Intersection of Lines
Solve line equations together for intersection; a parameter can describe a family through a point.
Learning objectives
- State the rule for family and intersection of lines.
- Solve a family and intersection of lines problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Solve line equations together for intersection; a parameter can describe a family through a point.
Formula
y=4 and x-y
Where / symbols
- Family and intersection of lines
- Solve line equations together for intersection; a parameter can describe a family through a point.
CONCEPT AND RULE
Solve line equations together for intersection; a parameter can describe a family through a point.
METHOD
For family and intersection of lines, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
x+y=4 and x-y=2 meet at (3,1).
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve family and intersection of lines
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Worked example
- Worked example:
- x+y=4 and x-y=2 meet at (3,1).
In simple words
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Key points
- Family and intersection of lines
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Family and Intersection of Lines
Sticky Notes · Formula and Worked Revision
Core Idea
- Solve line equations together for intersection; a parameter can describe a family through a point.
Rule / Formula
- Solve line equations together for intersection; a parameter can describe a family through a point.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- x+y=4 and x-y=2 meet at (3,1).
Common Error
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
FBISE Exam Tip
- Show the formula, substitutions, algebra, restrictions, and final answer; method marks need visible reasoning.
60-second revision
- Solve line equations together for intersection; a parameter can describe a family through a point.
- Worked pattern: x+y=4 and x-y=2 meet at (3,1).
- Final check: domain, sign, notation, units, and reasonableness.
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.