MathematicsChapter 6: Analytical Geometry
Equation of A Line
Point-slope form y-y1=m(x-x1) is safest when one point and slope are known.
Learning objectives
- State the rule for equation of a line.
- Solve a equation of a line problem step by step.
- Check the result, restrictions, notation, and units.
Definition
Point-slope form y-y1=m(x-x1) is safest when one point and slope are known.
Formula
y1=m(x-x1) is safest when one point and slo
Where / symbols
- Equation of a line
- Point-slope form y-y1=m(x-x1) is safest when one point and slope are known.
CONCEPT AND RULE
Point-slope form y-y1=m(x-x1) is safest when one point and slope are known.
METHOD
For equation of a line, 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
Slope 3 through (2,-1): y+1=3(x-2).
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 equation of a line
- 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:
- Slope 3 through (2,-1): y+1=3(x-2).
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
- Equation of a line
- rule
- worked example
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Equation of A Line
Sticky Notes · Formula and Worked Revision
Core Idea
- Point-slope form y-y1=m(x-x1) is safest when one point and slope are known.
Rule / Formula
- Point-slope form y-y1=m(x-x1) is safest when one point and slope are known.
Method
- Identify givens and restrictions.
- Write the rule.
- Substitute and simplify.
- Check the result.
Worked Example
- Slope 3 through (2,-1): y+1=3(x-2).
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
- Point-slope form y-y1=m(x-x1) is safest when one point and slope are known.
- Worked pattern: Slope 3 through (2,-1): y+1=3(x-2).
- Final check: domain, sign, notation, units, and reasonableness.
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