# Question #e45fb

Jan 22, 2018

Yes slopes are equal

#### Explanation:

Any line can be expressed as $y = m x + c$ where $m$ is the slope of the line
Hence here the slope of the line is
$3 y = 4 x - 12$
So $y = \frac{4}{3} x - 4$
Slope is $\frac{4}{3}$
Now for finding the slope of the line formed by the other 2 points we use $m = \frac{y 2 - y 1}{x 2 - x 1}$
So substituting the values we get $m = \frac{0 - 4}{- 3 - 0} = \frac{4}{3}$
Therefore the slopes are equal hence the lines formed are parallel
Hope u find it helpful :)

Jan 22, 2018

See below

#### Explanation:

Let the lines be ${L}_{1}$ and ${L}_{2}$ such that,
${L}_{1} \implies 4 x - 3 y = 12$

For ${L}_{2}$,
using two point form (as 2 points are given),

$\frac{y - 0}{x - \left(- 3\right)} = \frac{0 - 4}{- 3 - 0}$
$\implies \frac{y}{x + 3} = \frac{4}{3}$

${L}_{2} \implies 4 x - 3 y = - 12$

POINT TO REMEMBER :-
If the slopes of the lines are equal then, the lines are parallel or coincident.

From ${L}_{1}$,
$y = \frac{4}{3} x - 4$

From ${L}_{2}$,
$y = \frac{4}{3} x + 4$

We can clearly see that, the slopes of both the lines are equal,
i.e., $m = \frac{4}{3}$

$\therefore$ We conclude that the lines are parallel as their slopes are
equal.