Answer:
The equation of the line is ![y=-5x+12](https://tex.z-dn.net/?f=y%3D-5x%2B12)
Step-by-step explanation:
Step 1
Find the slope of the given line
we have
![10x+2y=-2](https://tex.z-dn.net/?f=10x%2B2y%3D-2)
Isolate the variable y
![2y=-10x-2](https://tex.z-dn.net/?f=2y%3D-10x-2)
![y=-5x-1](https://tex.z-dn.net/?f=y%3D-5x-1)
The slope of the given line is
![m=-5](https://tex.z-dn.net/?f=m%3D-5)
Step 2
Find the slope of the line that is parallel to the given line
we know that
if two lines are parallel, then their slopes are the same
so
![m1=m2](https://tex.z-dn.net/?f=m1%3Dm2)
----> slope of the given line
----> slope of the line parallel to the given line
Step 3
Find the equation of the line parallel to the given line that passes through the point ![(0,12)](https://tex.z-dn.net/?f=%280%2C12%29)
we know that
the equation of the line in slope-intercept form is equal to
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope of the line
b is the y-intercept (value of y when the value of x is equal to zero)
In this problem we have
-------> this is the y-intercept
so
![b=12](https://tex.z-dn.net/?f=b%3D12)
substitute
the equation of the line is
![y=-5x+12](https://tex.z-dn.net/?f=y%3D-5x%2B12)