Read y = mx + b and check the intercept cases
Read slope m and y-intercept b · Generate coordinates by substitution · Handle horizontal lines when finding x-intercepts
Section Paper 2 · Historical Extended · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Slope
- Linear expressions
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Read slope m and y-intercept b
- Generate coordinates by substitution
- Handle horizontal lines when finding x-intercepts
Two roles in one equation
In y=mx+b, m is the slope and the point (0,b) is the y-intercept. For y=−2x+3, m=−2 and the y-intercept is (0,3). Substitute an x value to obtain y; do not confuse the constant b with the x-intercept. For m≠0, setting y=0 gives x=−b/m.
Not every line has one x-intercept
For y=5, slope is zero and the line never reaches y=0. For y=0, every point on the line is on the x-axis, so there is no single x-intercept. A vertical line cannot be expressed as y=mx+b with a finite m. Positive m makes y increase as x increases, and negative m makes it decrease.
Sources for this lesson
Pause and explain
In y=−2x+3, which point is the y-intercept?
Worked example
For y=−2x+3, find slope and both axis intercepts.
Show the worked solution
- Slope is −2 and y-intercept is (0,3).
- Set 0=−2x+3 to get x=3/2.
Answer Slope −2; y-intercept (0,3); x-intercept (3/2,0).
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For y=3x−4, state slope and y-intercept, then find y when x=2.
Give me a hint
Read the coefficients and substitute.
Compare my reasoning
- m=3 and y-intercept=(0,−4).
- At x=2, y=6−4=2.
Slope 3; y-intercept (0,−4); y=2.
Look for these in your work
- Identify each coefficient
- Verify a point by substitution
Find the axis intercepts of y=(1/2)x−2.
Give me a hint
Set x=0 for one axis and y=0 for the other.
Compare my reasoning
- At x=0, y=−2.
- At y=0, x=4.
Y-intercept (0,−2); x-intercept (4,0).
Look for these in your work
- Use the correct zero coordinate
- Solve the remaining equation
Compare the x-intercepts of y=5 and y=0. Why is x=−b/m not available?
Give me a hint
Both equations have m=0.
Compare my reasoning
- y=5 has no point on the x-axis.
- y=0 is the whole x-axis; dividing by zero would be invalid in either case.
y=5: none; y=0: every point of the x-axis, not one intercept.
Look for these in your work
- Check the zero-slope case
- Do not divide by zero
Common mistakes
- b is the y-intercept value, not the x-intercept.
- Do not divide by m when m=0.
What can you explain now?
In y=−2x+3, which point is the y-intercept?
Compare with the explanation
(0,3).
The y-axis has x=0; substitution gives y=3.
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Make it stick
In y=−2x+3, which point is the y-intercept?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.