Equations of Linear Graphs (Copy)
Question 1
Find the gradient and y-intercept of the line y = 3x + 2.
Question 2
Find the gradient and y-intercept of the line y = –2x + 5.
Question 3
Find the gradient and y-intercept of the line 4x + 2y = 10. Write the equation in the form y = mx + c.
Question 4
A line passes through the point (0,4) and has gradient –3. Write its equation.
Question 5
A line passes through the point (0,–2) with gradient ½. Write its equation.
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
The equation of a line is 5x + 4y = 8. Find its gradient and y-intercept.
Question 7
The line goes through (2,5) with gradient 2. Write its equation.
Question 8
A line has equation y = –4x + 7. Find its gradient and intercepts.
Question 9
Find the equation of the line that passes through (–1,3) with gradient 3.
Question 10
A line is vertical and passes through x = –2. Write its equation.
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
A line is horizontal through y = 4. Write its equation.
Question 12
Find the equation of the line with gradient –2 passing through (0,–3).
Question 13
Find the gradient and y-intercept of the line y = 7 – 5x.
Question 14
The line passes through (1,2) and (3,6). Find its equation.
Question 15
The line passes through (–2,–5) and (0,–1). Find its equation.
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
Find the equation of the line parallel to y = 2x + 3 and passing through (0,–4).
Question 17
Find the equation of the line perpendicular to y = 3x + 2 and passing through (3,0).
Question 18
A line has gradient 5 and passes through (1,–2). Find its equation.
Question 19
Find the gradient and y-intercept of the line 2x – y = 7.
Question 20
Find the equation of the line through (4,1) with gradient –¾.
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 the equation of the line through (–3,2) with gradient 4.
Question 22
A line passes through (0,0) and (2,4). Find its equation.
Question 23
Find the equation of the line through (–2,4) with gradient –2.
Question 24
A line has equation 3x – 2y = 6. Write it in form y = mx + c and find its gradient.
Question 25
Find the equation of the line with gradient â…“ through point (3,2).
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
Question 26
Find the equation of the line perpendicular to y = –2x + 5 passing through (0,0).
Question 27
A line passes through (6,–2) and (–6,–8). Find its equation.
Question 28
The equation of a line is y = ½x – 6. Find gradient and intercepts.
Question 29
Find the equation of the line through (1,1) and parallel to y = –3x + 4.
Question 30
Find the equation of the line through (–1,–4) and (3,8).
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
1.
y = 3x + 2 → Gradient = 3, y-intercept = 2.
2.
y = –2x + 5 → Gradient = –2, y-intercept = 5.
3.
4x + 2y = 10 → y = –2x + 5 → Gradient = –2, y-intercept = 5.
4.
Through (0,4), gradient –3 → y = –3x + 4.
5.
Through (0,–2), gradient ½ → y = ½x – 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
6.
5x + 4y = 8 → y = –5/4x + 2 → Gradient = –5/4, y-intercept = 2.
7.
Through (2,5), gradient 2 → equation: y – 5 = 2(x – 2) → y = 2x + 1.
8.
y = –4x + 7 → Gradient = –4, y-intercept = 7.
x-intercept: 0 = –4x + 7 → x = 7/4.
9.
Through (–1,3), gradient 3 → y – 3 = 3(x + 1) → y = 3x + 6.
10.
Vertical line through x = –2 → equation is x = –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
11.
Horizontal line through y = 4 → equation is y = 4.
12.
Through (0,–3), gradient –2 → y = –2x – 3.
13.
y = 7 – 5x → rearrange: y = –5x + 7 → Gradient = –5, intercept = 7.
14.
Points (1,2), (3,6): Gradient = (6–2)/(3–1) = 4/2 = 2.
Equation: y – 2 = 2(x – 1) → y = 2x.
15.
Points (–2,–5), (0,–1): Gradient = (–1–(–5))/(0–(–2)) = 4/2 = 2.
Equation: y + 5 = 2(x + 2) → y = 2x – 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
16.
Parallel to y = 2x + 3, gradient = 2, through (0,–4) → y = 2x – 4.
17.
Perpendicular to y = 3x + 2 → slope = –1/3.
Through (3,0): y – 0 = –1/3(x – 3) → y = –1/3x + 1.
18.
Gradient 5, through (1,–2): y + 2 = 5(x – 1) → y = 5x – 7.
19.
2x – y = 7 → y = 2x – 7 → Gradient = 2, y-intercept = –7.
20.
Through (4,1), slope –¾: y – 1 = –¾(x – 4) → y = –¾x + 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
21.
Through (–3,2), slope 4: y – 2 = 4(x + 3) → y = 4x + 14.
22.
Through (0,0), (2,4): Gradient = (4–0)/(2–0) = 2.
Equation: y = 2x.
23.
Through (–2,4), slope –2: y – 4 = –2(x + 2) → y = –2x.
24.
3x – 2y = 6 → –2y = –3x + 6 → y = (3/2)x – 3.
Gradient = 1.5, intercept = –3.
25.
Through (3,2), slope ⅓: y – 2 = ⅓(x – 3) → y = ⅓x + 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
26.
Perpendicular to y = –2x + 5 → slope = ½.
Through (0,0): y = ½x.
27.
(6,–2), (–6,–8): Gradient = (–8–(–2))/(–6–6) = –6/–12 = ½.
Equation: y + 2 = ½(x – 6) → y = ½x – 5.
28.
y = ½x – 6 → Gradient = ½, intercept = –6.
x-intercept: 0 = ½x – 6 → x = 12.
29.
Parallel to y = –3x + 4 → slope = –3.
Through (1,1): y – 1 = –3(x – 1) → y = –3x + 4.
30.
Points (–1,–4), (3,8): Gradient = (8–(–4))/(3–(–1)) = 12/4 = 3.
Equation: y + 4 = 3(x + 1) → y = 3x – 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