Answer:
The equation of the line is [tex]y=-5x+12[/tex]
Step-by-step explanation:
Step 1
Find the slope of the given line
we have
[tex]10x+2y=-2[/tex]
Isolate the variable y
[tex]2y=-10x-2[/tex]
[tex]y=-5x-1[/tex]
The slope of the given line is
[tex]m=-5[/tex]
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
[tex]m1=m2[/tex]
[tex]m1=-5[/tex] ----> slope of the given line
[tex]m2=-5[/tex] ----> 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 [tex](0,12)[/tex]
we know that
the equation of the line in slope-intercept form is equal to
[tex]y=mx+b[/tex]
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
[tex]m=-5[/tex]
[tex]Point(0,12)[/tex] -------> this is the y-intercept
so
[tex]b=12[/tex]
substitute
the equation of the line is
[tex]y=-5x+12[/tex]
