5.5 Parallel Lines (Part 1)

Posted on April 23, 2020 by user

5.5 Parallel Lines (Part 1)

(A) Gradient of parallel lines

1. Two straight lines are
parallel if they have
the same gradient.

If PQ // RS,

then m_PQ = m_RS

2. If two straight lines have

the same gradient, then

they are parallel.

If m_AB = m_CD

then AB // CD

Example 1:

Determine whether the two straight lines are parallel.

(a) 2y – 4x = 6

y = 2x – 5

(b) 2y = 3x –4

3y = 2x +12

Solution:

(a)

2y – 4x = 6

2y = 6 + 4x

y = 2x + 3, m₁= 2

y = 2x – 5, m₂ = 2

m₁= m₂

Therefore, the two straight lines are parallel.

(b)

\begin{array}{l} 2 y = 3 x - 4 \\ y = \frac{3}{2} x - 2, m_{1} = \frac{3}{2} \\ 3 y = 2 x + 12 \\ y = \frac{2}{3} x + 4, m_{2} = \frac{2}{3} \\ m_{1} \neq m_{2} \\ ∴ The two straight lines are not parallel . \end{array}