Can you use the points A, B and C to verify that the slope of this line is indeed −5?
Answer: Yes. AB: −2 − 31 − 0 = −5; CA: 3 − 80 − (−1) = −5; CB: −2 − 81 − (−1) = −102 = −5. All three give −5.
Step-by-step solution
Idea: Slope = y2 − y1x2 − x1. Work it out for every pair of the three points; each must give −5.
- The points are A(0, 3), B(1, −2), C(−1, 8) on y = −5x + 3.½ mark
- A to B: −2 − 31 − 0 = −51 = −5.½ mark
- C to A: 3 − 80 − (−1) = −51 = −5.½ mark
- C to B: −2 − 81 − (−1) = −102 = −5. Every pair gives −5, so the slope is indeed −5.½ mark
Yes: slopes of AB, CA and CB are all −5.
Check: This matches m = −5 read directly from y = −5x + 3 ✓.
Answer to write in the exam
Slope AB = −2 − 31 − 0 = −5
Slope CA = 3 − 80 − (−1) = −5
Slope CB = −2 − 81 − (−1) = −102 = −5
∴ Slope of the line = −5
Common mistakes that cost marks
- Writing 0 − (−1) as −1, giving +5.
- Computing 8 − (−2)1 − (−1) (points in different orders on top and bottom), which gives +5.
How this can come in the exam
Short answer (2 marks)
Points P(0, −1), Q(2, 5) and R(−1, −4) lie on y = 3x − 1. Verify the slope using two different pairs.
Show answer
PQ: 5 − (−1)2 − 0 = 3 (1 mark). RQ: 5 − (−4)2 − (−1) = 93 = 3 (1 mark).Try one yourself
Verify that the slope of y = 2x − 4 is 2 using its points (0, −4) and (3, 2).
Show answer
2 − (−4)3 − 0 = 63 = 2 ✓.
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