Final answer:
To find the equation of a line parallel to a given line and passing through a specific point, we need the slope of the given line. Assuming the slope is 1, which aligns with the positive example slope, the correct equation for the line through point (14, -14) would be y = x - 28, which does not match any provided options. There might be an error in the provided options or additional context is necessary.
Step-by-step explanation:
The student asked to find the equation of the line that passes through the point (14, -14) and is parallel to a given line. To find this equation, we need to determine the slope of the given line since parallel lines have the same slope. From the information provided, for example, 'y = −173.5 + 4.83x' and 'Figure A1 Slope and the Algebra of Straight Lines', we understand that the slope of the line (m) is the key to finding the parallel line's equation. Since no specific slope is provided for the given line in this case, we would use the slope from the general example, which could be considered as a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis (m=3). However, given the options, it's clear that the slope must be either positive or negative one, since none of the options provided has a slope of 3.
Option 3 'y = x - 14' and Option 4 'y = -x - 14' both have slopes of 1 and -1, respectively. Therefore, to find the correct equation, we compare these options with the slope of the given line if known. Assuming that the given line has a slope of 1, based on the positive slope of 4.83 in the reference 'y = -173.5 + 4.83x', the parallel line would also have a slope of 1. Then, using the point (14, -14), we can plug it into the slope-intercept form of the equation, y = mx + b, where m is the slope and we solve for b, the y-intercept.
Putting the values into the equation, -14 = 1(14) + b, we get -14 = 14 + b. To find b, we subtract 14 from both sides to get b = -28. Thus, the equation of the line is y = 1x - 28. Unfortunately, this option was not provided among the choices, indicating a potential misunderstanding or an error in the options given or the question context. For the given options to align with the example slope, additional information would be required to definitively determine the correct slope and answer.