5.5 Parallel Lines (Sample Questions)

Example 1:

The straight lines MN and PQ in the diagram above are parallel. Find the value of q.

Solution:
If two lines are parallel, their gradients are equal.
m1 = m2
mMN = mPQ
$\begin{array}{l}\text{using gradient formula}\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}\\ \frac{9-4}{5-\left(-1\right)}=\frac{q-\left(-5\right)}{5-\left(-7\right)}\\ \frac{5}{6}=\frac{q+5}{12}\end{array}$
60 = 6q + 30
6q = 30
q = 5