Final answer:
The line parallel to the line represented by the equation x - 2y = 7 has the same slope. Option b) x - 2y = 0 is parallel as it can be written in slope-intercept form as y = (1/2)x, having the same slope of 1/2.
Step-by-step explanation:
The student's question concerns identifying the equation of a line parallel to a given line. For two lines to be parallel, they must have the same slope. Considering the original line's equation is x - 2y = 7, we need to find an equation among the options that has the same slope but a different y-intercept. The standard form for a line's equation is Ax + By = C, where A/B is the slope when the equation is rearranged into the slope-intercept form, y = mx + b.
So, the original equation can be rearranged to y = (1/2)x - (7/2), which gives a slope of 1/2. Comparing the slope of the options provided, the equation that also has a slope of 1/2 and therefore is parallel to the original line is b) x - 2y = 0 since it can be rearranged to y = (1/2)x which has the same slope as the original line.