MathematicsChapter 6: Analytical Geometry
Parallel and Perpendicular Lines
Parallel nonvertical lines have equal slopes; perpendicular slopes multiply to -1.
Learning objectives
- State the rule for parallel and perpendicular lines.
- Solve a parallel and perpendicular lines problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Parallel nonvertical lines have equal slopes; perpendicular slopes multiply to -1.
Formula
y=2x+1 has slope -12.
Where / symbols
- Parallel and perpendicular lines
- Parallel nonvertical lines have equal slopes; perpendicular slopes multiply to -1.
CONCEPT AND RULE
Parallel nonvertical lines have equal slopes; perpendicular slopes multiply to -1.
METHOD
For parallel and perpendicular 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
A line perpendicular to y=2x+1 has slope -12.
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 parallel and perpendicular 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:
- A line perpendicular to y=2x+1 has slope -12.
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
- Parallel and perpendicular lines
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Parallel and Perpendicular Lines
Sticky Notes · Formula and Worked Revision
Core Idea
- Parallel nonvertical lines have equal slopes; perpendicular slopes multiply to -1.
Rule / Formula
- Parallel nonvertical lines have equal slopes; perpendicular slopes multiply to -1.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- A line perpendicular to y=2x+1 has slope -12.
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
- Parallel nonvertical lines have equal slopes; perpendicular slopes multiply to -1.
- Worked pattern: A line perpendicular to y=2x+1 has slope -12.
- Final check: domain, sign, notation, units, and reasonableness.
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