Drawing Linear Graph (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Drawing and Interpreting Straight-Line Graphs (y = mx + c)
Includes Full Worked Solutions
Paper 1 – Non-Calculator Section
Q1.
The equation of a line is y = 2x – 3.
a) State the gradient and the y-intercept.
b) Find the value of y when x = 4.
Solution:
a) Gradient (m) = 2, y-intercept (c) = –3
b) Substitute x = 4:
y = 2(4) – 3 = 8 – 3 = 5
Answer:
a) Gradient = 2, y-intercept = –3
b) y = 5
Q2.
The equation of a line is y = –3x + 2.
Find the coordinates of two points you would plot to draw this line.
Solution:
Choose x-values: x = 0 and x = 1
- x = 0 → y = –3(0) + 2 = 2 → (0, 2)
- x = 1 → y = –3(1) + 2 = –1 → (1, –1)
Answer: (0, 2) and (1, –1)
Q3.
The line passes through the points (0, 1) and (2, 5).
Find the gradient of the line.
Solution:
Gradient = (change in y) ÷ (change in x)
= (5 – 1) ÷ (2 – 0) = 4 ÷ 2 = 2
Answer: Gradient = 2
Q4.
Without plotting, state whether the graph of y = –x + 4 slopes upwards or downwards.
Solution:
Gradient (m) = –1 → Negative gradient → Slopes downwards.
Answer: Downwards
Paper 2 – Calculator Allowed Section
Q5.
Complete the table of values for y = x + 2.
| x | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y |
Solution:
Substitute values:
- x = –2 → y = –2 + 2 = 0
- x = –1 → y = –1 + 2 = 1
- x = 0 → y = 0 + 2 = 2
- x = 1 → y = 1 + 2 = 3
- x = 2 → y = 2 + 2 = 4
Answer:
| x | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 0 | 1 | 2 | 3 | 4 |
Q6.
The equation of a straight line is y = 5.
Describe the line.
Solution:
y = 5 is a horizontal line through y = 5.
Answer: Horizontal line through y = 5
Q7.
Find the equation of the line that has a gradient of 4 and passes through the point (0, –2).
Solution:
Form: y = mx + c
Since gradient m = 4 and y-intercept c = –2,
Equation: y = 4x – 2
Answer: y = 4x – 2
Q8.
Which equation has a line with gradient –2 and y-intercept 3?
A) y = –2x + 3
B) y = 2x – 3
C) y = –2x – 3
D) y = 2x + 3
Solution:
Gradient = –2, y-intercept = 3 → Match A.
Answer: A
Q9.
The equation of a line is y = 0.5x – 1.
Find the y-value when x = –4.
Solution:
y = 0.5(–4) – 1 = –2 – 1 = –3
Answer: y = –3
Q10.
For the line y = –x – 2, find the coordinates where it crosses the y-axis.
Solution:
At y-intercept, x = 0
Substitute: y = –(0) – 2 = –2
Coordinates: (0, –2)
Answer: (0, –2)
This practice exam tests all CORE-level skills for straight-line graphs including interpreting equations, finding points, understanding gradient, and simple table completion — matching Paper 1 and 2 expectations.