Drawing Linear Graphs (Copy)
Question 1
Draw the graph of y = 2x + 3 for –3 ≤ x ≤ 3.
State the gradient and y-intercept.
Question 2
Sketch the line y = –x + 4 for –2 ≤ x ≤ 6.
Find the coordinates where the line crosses the axes.
Question 3
Plot the line y = –2x + 5 for –2 ≤ x ≤ 4.
State the intercepts on both axes.
Question 4
Draw the graph of y = 3 – 4x for –1 ≤ x ≤ 3.
Find the x-intercept.
Question 5
Sketch the line 3x + 2y = 6.
Find the x-intercept and y-intercept.
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 6
Draw y = 4x – 7 for –2 ≤ x ≤ 3.
State the gradient and intercepts.
Question 7
Sketch y = –3x + 2.
Find the coordinates of the x- and y-intercepts.
Question 8
Plot the line 2x + y = 4.
Find the intercepts.
Question 9
Sketch the line y = 5.
What type of line is this, and what is its gradient?
Question 10
Draw x = –2.
What kind of line is this, and what is its 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 11
Plot the line y = ½x + 1 for –4 ≤ x ≤ 4.
State its slope.
Question 12
Draw y = –2x – 3 for –3 ≤ x ≤ 3.
Find the intercepts.
Question 13
Sketch 4x – y = 8.
Find the intercepts.
Question 14
Draw y = 3x for –2 ≤ x ≤ 3.
What does the gradient tell you?
Question 15
Sketch y = –x – 2.
Find the equation of the line parallel to this one passing through (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
Question 16
Draw 2y + x = 8.
Find intercepts with both axes.
Question 17
Sketch y = –4x + 6.
Find where it cuts the x-axis.
Question 18
Draw y = 3x – 5.
Find the x- and y-intercepts.
Question 19
Plot 2x – 3y = 12.
Find intercepts.
Question 20
Sketch y = –2x.
How is this line different from y = 2x?
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
Draw y = x + 2.
Find where it crosses both axes.
Question 22
Sketch the line y = –5.
What is its equation in general form?
Question 23
Draw y = 2x – 4.
Find its slope and y-intercept.
Question 24
Plot the line x – y = 3.
Find its intercepts.
Question 25
Sketch y = ¼x – 2.
Find the gradient and intercept.
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
Plot y = –2x + 8.
Find x-intercept and y-intercept.
Question 27
Sketch 5x + y = 10.
Find intercepts.
Question 28
Draw y = –3x + 4.
Find slope and intercepts.
Question 29
Sketch x + 2y = 8.
Find where the line crosses the axes.
Question 30
Draw y = –x/2 + 5.
Find gradient and intercepts.
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.
y = 2x + 3
- Gradient = 2 (line rises 2 for every 1 across).
- y-intercept = (0,3).
2.
y = –x + 4
- y-intercept: (0,4).
- x-intercept: (4,0).
- Gradient = –1.
3.
y = –2x + 5
- y-intercept: (0,5).
- x-intercept: (2.5,0).
4.
y = 3 – 4x
- y-intercept: (0,3).
- For x-intercept: 0 = 3 – 4x → x = ¾.
5.
3x + 2y = 6
- x-intercept: set y=0 → x=2 → (2,0).
- y-intercept: set x=0 → y=3 → (0,3).
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
6.
y = 4x – 7
- Gradient = 4.
- y-intercept: (0,–7).
- x-intercept: 0 = 4x – 7 → x = 7/4.
7.
y = –3x + 2
- y-intercept: (0,2).
- x-intercept: (2/3,0).
8.
2x + y = 4
- y-intercept: (0,4).
- x-intercept: (2,0).
9.
y = 5
- Horizontal line through y=5.
- Gradient = 0.
10.
x = –2
- Vertical line at x = –2.
- Gradient undefined.
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.
y = ½x + 1
- Gradient = ½.
- y-intercept = (0,1).
12.
y = –2x – 3
- y-intercept = (0,–3).
- x-intercept: 0 = –2x – 3 → x = –1.5.
13.
4x – y = 8 → y = 4x – 8
- y-intercept: (0,–8).
- x-intercept: (2,0).
14.
y = 3x
- Gradient = 3 → line steeper than y=x.
- Passes through origin.
15.
y = –x – 2
- Gradient = –1, intercept = (0,–2).
- Parallel line through (0,5) → equation: y = –x + 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
16.
2y + x = 8 → y = –½x + 4
- y-intercept = (0,4).
- x-intercept: (8,0).
17.
y = –4x + 6
- y-intercept = (0,6).
- x-intercept: 0 = –4x + 6 → x = 1.5.
18.
y = 3x – 5
- y-intercept = (0,–5).
- x-intercept: (5/3,0).
19.
2x – 3y = 12 → y = (2/3)x – 4
- y-intercept = (0,–4).
- x-intercept = (6,0).
20.
y = –2x
- Gradient = –2 (falls as x increases).
- Different from y=2x (positive slope).
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.
y = x + 2
- y-intercept: (0,2).
- x-intercept: (–2,0).
22.
y = –5
- Horizontal line through y=–5.
- General form: 0x + y = –5.
23.
y = 2x – 4
- Gradient = 2.
- y-intercept: (0,–4).
24.
x – y = 3 → y = x – 3
- y-intercept = (0,–3).
- x-intercept = (3,0).
25.
y = ¼x – 2
- Gradient = ¼ (gentle slope).
- y-intercept: (0,–2).
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.
y = –2x + 8
- y-intercept = (0,8).
- x-intercept: 0 = –2x + 8 → x = 4.
27.
5x + y = 10 → y = –5x + 10
- y-intercept = (0,10).
- x-intercept = (2,0).
28.
y = –3x + 4
- Gradient = –3.
- y-intercept: (0,4).
- x-intercept: (4/3,0).
29.
x + 2y = 8 → y = –½x + 4
- y-intercept = (0,4).
- x-intercept = (8,0).
30.
y = –½x + 5
- Gradient = –½.
- y-intercept: (0,5).
- x-intercept: (10,0).
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