Answer: [tex]y=-5x+12[/tex] or [tex]5x+y=12[/tex]
Step-by-step explanation:
The given equation of a line: [tex]10x+2y=-2[/tex]
Rewrite equation of line in slope intercept form (y=mx+c) by subtracting 10 on both sides and then divide both sides by 2, we get
[tex]y=-5x-1[/tex]
Slope of line : m= -5 [Coefficient of x]
Since , the slope of two parallel lines are equal.
Then, slope of line parallel to given line= -5
Equation of a line passing through point (a,b) and has slope p is given by :-
[tex](y-b)=p(x-a)[/tex]
Similarly, Equation of a line passing through point (0,12) and has slope -5 is given by :-
[tex](y-12)=(-5)(x-0)\\\\\Rightarrow\ y-12=-5x\\\\\Rightarrow\ 5x+y=12[/tex]
