Final answer:
The equation of the line parallel to the given line and passing through (4,2) is y - 2 = 12(x - 4), assuming there's a typo and the given line should include 'x'.
Step-by-step explanation:
The question asks for the equation of a line that is parallel to another line and also passes through a specific point, written in point-slope form. To begin, we recognize that parallel lines have the same slope. The provided equation y = -3 + 12 does not follow the slope-intercept form y = mx + b, where 'm' is the slope. Here, the expression appears to lack a variable 'x', and it seems there might be a typo or an error in the transcription of the equation. Assuming that the correct form of the equation should include 'x' (for instance, y = 12x - 3), we would take the slope 'm' to be 12. The point-slope form of the equation is y - y1 = m(x - x1), where (x1, y1) is the given point and 'm' is the slope. Since we need the line parallel to the given one and passing through (4,2), our slope is 12. Thus, substituting the values we have, the point-slope form of the equation is y - 2 = 12(x - 4).