Final answer:
The equation of the line parallel to 10x + 2y = 2 and passing through the point (0, 12) is y = -5x + 12. The line has the same slope as the given line, which is -5, and its y-intercept is 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 10x + 2y = 2 and passing through the point (0, 12), we first need to find the slope of the given line. We rearrange the equation into slope-intercept form: 2y = -10x + 2, which simplifies to y = -5x + 1. This means the slope, m, of the given line is -5. Since parallel lines have the same slope, the slope of the new line will also be -5.
Now, using the slope -5 and the point (0, 12), where the new line crosses the y-axis, we plug into the slope-intercept form of the equation to get y = -5x + 12. Therefore, the correct equation representing the line that is parallel to the given line and passes through (0, 12) is A) y = -5x + 12.