MathematicsChapter 8: Geometry of Straight Lines
Intercept Form
x/a + y/b = 1 meets the x-axis at (a, 0) and the y-axis at (0, b).
Learning objectives
- Define and explain intercept form.
- Apply intercept form to a focused FBISE question.
- Check the answer for correct terms, evidence, working, and units.
Definition
xa + yb = 1 meets the x-axis at (a, 0) and the y-axis at (0, b). Example: x/2 + y/3 = 1 cuts at (2, 0) and (0, 3). You cannot use this form for a line through the origin (both intercepts would be 0 and you would divide by zero), nor for a line parallel to an axis (one intercept is missing). Multiply through by a*b to reach a linear equation without denominators.
Formula
b = 1 meets the x-axis at (a
Where / symbols
- Intercept Form
- x/a + y/b = 1 meets the x-axis at (a, 0) and the y-axis at (0, b). Example: x/2 + y/3 = 1 cuts at (2, 0) and (0, 3). You cannot use this form for a line through the origin (both intercepts would be 0 and you would divide by zero), nor for a line parallel to an axis (one intercept is missing). Multiply through by a*b to reach a linear equation without denominators.
Relationship
- xa + yb = 1
Overview
Learn the idea, then use it:
Core Understanding
xa + yb = 1 meets the x-axis at (a, 0) and the y-axis at (0, b). Example: x/2 + y/3 = 1 cuts at (2, 0) and (0, 3). You cannot use this form for a line through the origin (both intercepts would be 0 and you would divide by zero), nor for a line parallel to an axis (one intercept is missing). Multiply through by a*b to reach a linear equation without denominators.
Examples x/a + y/b = 1 · (a, 0) · (0, b) · INTERCEPT FORM: x/a + y/b = 1 meets the x-axis at (a, 0) and the y-axis at (0, b). Example: x/2 + y/3 = 1 cuts at (2, 0) and (0, 3). You
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 — INTERCEPT FORM
xa + yb = 1 meets the x-axis at (a, 0) and the y-axis at (0, b). Example: x/2 + y/3 = 1 cuts at (2, 0) and (0, 3). You cannot use this form for a line through the origin (both intercepts would be 0 and you would divide by zero), nor for a line parallel to an axis (one intercept is missing). Multiply through by a*b to reach a linear equation without denominators.
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 intercept form with a neighbouring idea that uses a different definition, rule, or method.
Key points
- xa + yb = 1
- (a, 0)
- (0, b)
Exam preparation
Exam Focus
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.Intercept Form
Sticky Notes · Quick Revision
Core Idea
- xa + yb = 1 meets the x-axis at (a, 0) and the y-axis at (0, b).
Key Points
- xa + yb = 1
- (a, 0)
- (0, b)
Simple Check
- Explain intercept form 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 intercept form 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
- xa + yb = 1 meets the x-axis at (a, 0) and the y-axis at (0, b).
- xa + yb = 1
- (a, 0)
- (0, b)
Did you understand this topic?
Your answer is saved with your learning record. It does not mark the topic as mastered.