Gradient of Linear Graphs (Copy)
Practice Questions — 3.3 Gradient of Linear Graphs (30 Questions)
Question 1
Find the gradient of the line passing through points A(0,0) and B(4,8).
Question 2
Calculate the gradient of the line through P(–3,2) and Q(5,6).
Question 3
The line passes through (1,4) and (3,10).
Find its gradient.
Question 4
Find the gradient of the line passing through (–2,–1) and (2,7).
Question 5
Line passes through (0,5) and (5,0).
Find gradient.
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Question 6
Find gradient of line through (–4,3) and (0,–5).
Question 7
Line passes through (2,–1) and (6,–9).
Calculate gradient.
Question 8
Find the gradient of the line joining (7,0) and (7,5).
Question 9
Line passes through (–3,–3) and (3,–3).
Find gradient.
Question 10
Find gradient of line through (–6,4) and (–2,–8).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 11
Find gradient of line through (1,1) and (2,2).
Question 12
Find gradient of line through (–5,–1) and (5,19).
Question 13
Find gradient of line through (0,–2) and (4,–10).
Question 14
Line passes through (–7,6) and (–7,–4).
Find gradient.
Question 15
Find gradient of line through (–2,–6) and (4,–6).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 16
Line passes through (–1,2) and (3,14).
Find gradient.
Question 17
Find gradient of line through (–8,–2) and (–4,10).
Question 18
Find gradient of line through (2,–3) and (–2,9).
Question 19
Find gradient of line through (0,–5) and (5,–20).
Question 20
Line passes through (–3,7) and (9,–5).
Find gradient.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 21
Find gradient of line through (0,3) and (6,3).
Question 22
Find gradient of line through (–4,–4) and (–2,8).
Question 23
Find gradient of line through (1,7) and (7,1).
Question 24
Line passes through (–9,–5) and (–3,–1).
Find gradient.
Question 25
Find gradient of line through (–1,–1) and (2,8).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
Question 26
Find gradient of line through (–10,5) and (0,–15).
Question 27
Find gradient of line through (–6,–6) and (6,6).
Question 28
Find gradient of line through (–5,–2) and (–1,–10).
Question 29
Line passes through (3,9) and (–3,–9).
Find gradient.
Question 30
Find gradient of line through (0,0) and (8,–4).
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
1.
A(0,0), B(4,8) → m = (8–0)/(4–0) = 8/4 = 2.
2.
P(–3,2), Q(5,6) → m = (6–2)/(5–(–3)) = 4/8 = 0.5.
3.
(1,4), (3,10) → m = (10–4)/(3–1) = 6/2 = 3.
4.
(–2,–1), (2,7) → m = (7–(–1))/(2–(–2)) = 8/4 = 2.
5.
(0,5), (5,0) → m = (0–5)/(5–0) = –5/5 = –1.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
6.
(–4,3), (0,–5) → m = (–5–3)/(0–(–4)) = –8/4 = –2.
7.
(2,–1), (6,–9) → m = (–9–(–1))/(6–2) = –8/4 = –2.
8.
(7,0), (7,5) → denominator = 0 → gradient is undefined (vertical line).
9.
(–3,–3), (3,–3) → numerator = 0 → gradient = 0 (horizontal line).
10.
(–6,4), (–2,–8) → m = (–8–4)/(–2–(–6)) = –12/4 = –3.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
11.
(1,1), (2,2) → m = (2–1)/(2–1) = 1/1 = 1.
12.
(–5,–1), (5,19) → m = (19–(–1))/(5–(–5)) = 20/10 = 2.
13.
(0,–2), (4,–10) → m = (–10–(–2))/(4–0) = –8/4 = –2.
14.
(–7,6), (–7,–4) → vertical line → gradient = undefined.
15.
(–2,–6), (4,–6) → horizontal line → gradient = 0.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
16.
(–1,2), (3,14) → m = (14–2)/(3–(–1)) = 12/4 = 3.
17.
(–8,–2), (–4,10) → m = (10–(–2))/(–4–(–8)) = 12/4 = 3.
18.
(2,–3), (–2,9) → m = (9–(–3))/(–2–2) = 12/–4 = –3.
19.
(0,–5), (5,–20) → m = (–20–(–5))/(5–0) = –15/5 = –3.
20.
(–3,7), (9,–5) → m = (–5–7)/(9–(–3)) = –12/12 = –1.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
21.
(0,3), (6,3) → horizontal line → gradient = 0.
22.
(–4,–4), (–2,8) → m = (8–(–4))/(–2–(–4)) = 12/2 = 6.
23.
(1,7), (7,1) → m = (1–7)/(7–1) = –6/6 = –1.
24.
(–9,–5), (–3,–1) → m = (–1–(–5))/(–3–(–9)) = 4/6 = 2/3.
25.
(–1,–1), (2,8) → m = (8–(–1))/(2–(–1)) = 9/3 = 3.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course
26.
(–10,5), (0,–15) → m = (–15–5)/(0–(–10)) = –20/10 = –2.
27.
(–6,–6), (6,6) → m = (6–(–6))/(6–(–6)) = 12/12 = 1.
28.
(–5,–2), (–1,–10) → m = (–10–(–2))/(–1–(–5)) = –8/4 = –2.
29.
(3,9), (–3,–9) → m = (–9–9)/(–3–3) = –18/–6 = 3.
30.
(0,0), (8,–4) → m = (–4–0)/(8–0) = –4/8 = –0.5.
Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course