Equations of Linear Graph (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Finding and Interpreting Straight-Line Equations (y = mx + c and x = k)
Includes Full Worked Solutions
Paper 1 – Non-Calculator Section
Q1.
Find the gradient and y-intercept of the line given by the equation:
y = 4x – 7
Solution:
- Gradient (m) = 4
- Y-intercept (c) = –7
Answer:
Gradient = 4
Y-intercept = –7
Q2.
State the equation of the vertical line passing through x = –3.
Solution:
Equation of a vertical line is simply:
x = –3
Answer: x = –3
Q3.
A straight line passes through the points (0, 5) and (2, 9).
Find the equation of the line.
Solution:
- Find the gradient (m):
m=9−52−0=42=2m = frac{9 – 5}{2 – 0} = frac{4}{2} = 2
- Find y-intercept (c):
Already given (0, 5) → y-intercept = 5 - Equation:
y = 2x + 5
Answer: y = 2x + 5
Q4.
Find the equation of a line that passes through (0, –2) and has a gradient of –5.
Solution:
y-intercept = –2 (since x = 0)
Gradient = –5
Equation:
y = –5x – 2
Answer: y = –5x – 2
Q5.
Find the equation of the straight line with gradient 0 and passing through (0, 3).
Solution:
- Gradient = 0 → horizontal line
- Horizontal line at y = constant
Equation:
y = 3
Answer: y = 3
Paper 2 – Calculator Allowed Section
Q6.
The line passes through (1, 4) and (5, 8). Find its equation.
Solution:
- Find gradient:
m=8−45−1=44=1m = frac{8 – 4}{5 – 1} = frac{4}{4} = 1
- Find y-intercept using (1, 4):
Substitute into y = mx + c:
4 = 1(1) + c → c = 3
Equation:
y = x + 3
Answer: y = x + 3
Q7.
Which of the following lines has a gradient of –2?
A) y = 2x + 1
B) y = –2x + 3
C) y = x – 2
D) y = –x + 2
Solution:
B has gradient –2.
Answer: B) y = –2x + 3
Q8.
A line passes through (–2, 1) and (2, –3).
Find its equation.
Solution:
- Gradient:
m=−3−12−(−2)=−44=−1m = frac{-3 – 1}{2 – (-2)} = frac{-4}{4} = -1
- Find y-intercept using (–2, 1):
1 = –1(–2) + c
1 = 2 + c
c = 1 – 2 = –1
Equation:
y = –x – 1
Answer: y = –x – 1
Q9.
The equation of a line is y = –0.5x + 4.
Find:
a) the gradient
b) the y-intercept
Solution:
a) Gradient = –0.5
b) Y-intercept = 4
Answer:
a) –0.5
b) 4
Q10.
The equation of a line is x = 6.
Describe this line.
Solution:
- Vertical line passing through x = 6.
- No slope (undefined gradient).
Answer: Vertical line at x = 6
This exam fully matches CORE-level requirements: finding gradient and y-intercept from equations, writing full equations from points or descriptions, and interpreting vertical and horizontal lines.