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