Condition for Straight Lines in Plane to be Parallel/Examples/Arbitrary Example 1

Examples of Use of Condition for Straight Lines in Plane to be Parallel
Let $\LL_1$ be the straight line whose equation in general form is given as:
 * $3 x - 4 y = 7$

Let $\LL_2$ be the straight line parallel to $\LL_1$ which passes through the point $\tuple {1, 2}$.

The equation for $\LL_2$ is:
 * $3 x - 4 y = -5$

Proof
From Condition for Straight Lines in Plane to be Parallel, $\LL_2$ has an equation of the form:


 * $(1): \quad 3 x - 4 y = C$

We have that $\tuple {1, 2}$ is on $\LL_2$.

Hence substituting $x = 1$ and $y = 2$ into $(1)$:

Hence the result.