Final answer:
The equation of the line, in slope-intercept form, that is parallel to 10x + 2y = -2 and passes through (0, 12) is y = -5x + 12.
Step-by-step explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of a line parallel to the given line and passing through the point (0, 12), we need to use the fact that parallel lines have the same slope.
The equation of the given line is 10x + 2y = -2, which can be rewritten as 2y = -10x - 2 or y = -5x - 1. Since the slope is -5, the equation of the parallel line can be written as y = -5x + b.
To find the value of b, we substitute the coordinates of the given point (0, 12) into the equation and solve for b: 12 = -5(0) + b, which simplifies to b = 12.
Therefore, the equation of the line parallel to the given line and passing through the point (0, 12) is y = -5x + 12.