Question

A given line has the equation 10x+2y=-2.

Answer 1

The equation of a line of the slope-intersection form is given by:

$y = mx + b$

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:

$10x + 2y = -2\\2y = -10x-2\\y = -5x-1$

Thus, the slope of the line is -5.

Therefore a parallel line is of the form:

$y = -5x + b$

We replace the point $(0,12)$

$12 = -5 (0) + b\\12 = b$

Finally, the equation is of the form:

$y = -5x + 12$

Answer:

$5x + y = 12$