Final answer:
The equation of the new line parallel to the given lines and passing through the point (6, 4) is y = 4.83x - 24.98, using the slope of the line of best fit, which the parallel lines share.
Step-by-step explanation:
The equation of a line parallel to another given line Y2 = -173.5 + 4.83x − 2(16.4) and Y3 = -173.5 + 4.83x + 2(16.4), passing through the point (6, 4). These lines are parallel to the line of best fit y = -173.5 + 4.83x since they have the same slope. To be parallel to these lines, the new line must also have the same slope, which is 4.83. The line equation is y = mx + b, where m is the slope, and b is the y-intercept, the point where the line intersects the vertical axis.
To find the y-intercept of our new line, we use the point (6, 4) and the slope 4.83:
4 = 4.83(6) + b
b = 4 - (4.83 × 6)
b = 4 - 28.98
b = -24.98
Thus, the equation of the new line is y = 4.83x - 24.98, which is not present in the given options.