Final answer:
To determine whether line d is parallel to line e, we would need to compare the slopes of the two lines represented by their linear equations. Without additional information, we cannot choose which equation proves line d is parallel to line e.
Step-by-step explanation:
The question relates to determining the conditions under which 'line d' is parallel to 'line e'. This involves the concept of linear equations and their slopes. If two lines are parallel, their slopes must be equal. The slope of a line is represented by the coefficient of x in the linear equation y = mx + b, where m is the slope and b is the y-intercept.
The given equations 3x−4=0, 2x+5=0, x−2=0, and 4x+7=0 can be rearranged to express y as a function of x in the form y = mx + b. For example, 3x−4=0 can be rearranged to y = 3x by adding 4 to both sides and then subtracting 3x from both sides, which implies that the slope of this line is 3.
To prove that 'line d' is parallel to 'line e', we would need to know the slope of line e and then find the equation among the options with the same slope. However, without additional information about the slope of line e or the context in which these equations are used, we cannot definitively choose which of the provided equations would satisfy the condition for parallel lines.