CIE IGCSE Mathematics (0580) Parallel lines Study Notes - New Syllabus
CIE IGCSE Mathematics (0580) Parallel lines Study Notes
LEARNING OBJECTIVE
- Parallel Lines
Key Concepts:
- Parallel Lines
Parallel Lines
Two straight lines are parallel if they have the same gradient (slope). They never intersect and are always the same distance apart.
Key Fact:
If line A has the equation \( y = mx + c_1 \), then any line parallel to it has the equation \( y = mx + c_2 \), where \( m \) is the same, but \( c_2 \neq c_1 \).
Steps to Find the Equation of a Line Parallel to a Given Line:
- Identify the gradient \( m \) from the given line.
- Use the point given to substitute into \( y = mx + c \) and solve for \( c \).
- Write the final equation in the form \( y = mx + c \).
Example :
Find the equation of the line parallel to \( y = 4x – 1 \) that passes through the point (2, 5).
▶️ Answer/Explanation
Gradient \( m = 4 \) (same as the given line)
Use \( y = mx + c \) and point (2, 5): \( 5 = 4(2) + c \Rightarrow 5 = 8 + c \Rightarrow c = -3 \)
Answer: \( y = 4x – 3 \)
Example :
A line is parallel to \( y = -\frac{1}{2}x + 7 \) and passes through (0, –3). Find its equation.
▶️ Answer/Explanation
Gradient \( m = -\frac{1}{2} \)
Use point (0, –3): \( y = mx + c \Rightarrow -3 = -\frac{1}{2}(0) + c \Rightarrow c = -3 \)
Answer: \( y = -\frac{1}{2}x – 3 \)