Answer:
Option A is correct.
[tex]X+5Y=6[/tex]
Step-by-step explanation:
Given:
Two points are given (3,-6) and (-7,-4).
We need to find the line that is parallel to the line which is passes through the points (3,-6) and (-7,-4).
The slope of the line is.
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Now, we substitute all given value in above equation.
[tex]m = \frac{-4-(-6)}{-7-3}}[/tex]
[tex]m = \frac{-4+6)}{-10}}[/tex]
[tex]m = \frac{2)}{-10}}[/tex]
[tex]m = -\frac{1}{5}[/tex]
We know that the parallel lines has same slope, so we check the option one by one.
Option A,
[tex]X+5Y=6[/tex]
Now, we write the above equation in standard form [tex]y=mx +c[/tex].
[tex]5Y=-X+6[/tex]
[tex]Y = -\frac{1}{5}X+\frac{6}{5}[/tex]
Where [tex]m = -\frac{1}{5}[/tex]
The slope of the above line is [tex]-\frac{1}{5}[/tex], so the line [tex]X+5Y=6[/tex] is parallel to the line which is passes through the points (3,-6) and (-7,-4), so there is no need to check the other choices.
Therefore, Option A is correct.
