Consider the line 5x + y = 3. Rewrite it as y = −5x + 3. Can you now find its slope? What does it mean?
Answer: Slope m = −5: for every increase of 1 unit in x, y decreases by 5 units. The y-intercept d = 3, so the line crosses the y-axis at (0, 3).
Step-by-step solution
Idea: In y = mx + d the number multiplying x is the slope and the constant is the y-intercept.
- 5x + y = 3 ⇒ y = −5x + 3. Compare with y = mx + d: m = −5, d = 3.½ mark
- The slope is −5.½ mark
- Meaning: each time x goes up by 1, y goes down by 5, so the line falls steeply from left to right. E.g. x = 0 → y = 3; x = 1 → y = −2.½ mark
- d = 3 is the y-intercept: the line crosses the y-axis at (0, 3).½ mark
The slope is −5: y decreases by 5 for every 1-unit increase in x. The line meets the y-axis at (0, 3).
Check: Points (0, 3) and (1, −2): −2 − 31 − 0 = −5 ✓.
Answer to write in the exam
5x + y = 3 ⇒ y = −5x + 3
Comparing with y = mx + d: m = −5, d = 3
∴ Slope = −5: y decreases by 5 for each unit increase in x
y-intercept = 3: line cuts the y-axis at (0, 3)
Common mistakes that cost marks
- Reading the slope as 5 from 5x + y = 3 without first making y the subject.
- Thinking a slope of −5 means the line is “less steep” than slope 1. Its size, 5, makes it steeper; the minus sign only says it goes down.
How this can come in the exam
MCQ (1 mark)
The slope and y-intercept of 2x + y = 6 are
- 2 and 6
- −2 and 6
- −2 and 3
- 2 and −6
Show answer
(B) −2 and 6
y = −2x + 6.
Try one yourself
Find the slope and y-intercept of 3x + y = −4 and say what the slope means.
Show answer
y = −3x − 4: slope −3 (y drops 3 for each unit increase in x), y-intercept −4.
More questions like this
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