MathematicsChapter 8: Geometry of Straight Lines
Point-Slope
Start from m = rise/run = (y - y1)/(x - x1) and cross multiply to get y - y1 = m(x - x1).
Learning objectives
- Define and explain point-slope.
- Apply point-slope to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.
Mathematical form
m = rise/run
y1 = m(x - x1). That is point-slope
m=4 gives y-3
y=4x-5. If m
Where / symbols
- Point-Slope
- Start from m = rise/run = (y - y1)/(x - x1) and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.
Relationship
- y - y1 = m(x - x1)
Overview
Learn the idea, then use it:
Core Understanding
Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.
Examples y - y1 = m(x - x1) · through (x1, y1) · gradient m · POINT-SLOPE: Start from m = rise/run = (y - y1)/(x - x1) and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line
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 — POINT-SLOPE
Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1). That is point-slope: the line through (x1, y1) with gradient m. Example: through (2, 3) with m=4 gives y-3=4(x-2), which expands to y=4x-5. If m=0 you get the horizontal line y=y1.
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 point-slope with a neighbouring idea that uses a different definition, rule, or method.
Key points
- y - y1 = m(x - x1)
- through (x1, y1)
- gradient m
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Point-Slope
Sticky Notes · Quick Revision
Core Idea
- Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1).
Key Points
- y - y1 = m(x - x1)
- through (x1, y1)
- gradient m
Simple Check
- Explain point-slope 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 point-slope 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
- Start from m = rise/run = y - y1x - x1 and cross multiply to get y - y1 = m(x - x1).
- y - y1 = m(x - x1)
- through (x1, y1)
- gradient m
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.