The equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
If two lines are parallel then their slopes are equal.
We have the following line:
[tex]10x + 2y = -2\\2y = -10x-2\\y = -5x-1[/tex]
Thus, the slope of the line is -5.
Therefore a parallel line is of the form:
[tex]y = -5x + b[/tex]
We replace the point [tex](0,12)[/tex]
[tex]12 = -5 (0) + b\\12 = b[/tex]
Finally, the equation is of the form:
[tex]y = -5x + 12[/tex]
Answer:
[tex]5x + y = 12[/tex]
