Final answer:
The slope of a line parallel to -1/2x = 4y is -1/8, as found by rearranging the equation to slope-intercept form. Parallel lines have identical slopes, so any line parallel to this one will have a slope of -1/8.
Step-by-step explanation:
The slope of a line parallel to the line given by -1/2x = 4y can be found by first rewritting the equation in slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. To do this, we solve for y in terms of x, yielding y = -1/8x. Since the given line has a slope of -1/8, any line parallel to it must have the same slope, which is -1/8.
Keeping in mind that lines which are parallel have identical slopes, the slope of line Y2 = -173.5 + 4.83x − 2(16.4), and line Y3 = -173.5 + 4.83x + 2(16.4) is the same as the slope of the line of best fit, which is 4.83. These examples demonstrate how consistent the slope is for parallel lines regardless of their y-intercepts.