In which pair do both lines have equal slopes but different y-intercepts?

Correct answer: y = 2x + 5 and y = 2x − 3

The governing concept is slope-intercept form, y = mx + c, where m is the slope and c is the y-intercept. In option A, both equations have m = 2, so their slopes are equal, while their y-intercepts are 5 and −3, which are different. These are therefore distinct parallel lines and have no common point. In option B, the slopes are 2 and −2, so the slopes are not equal. In option C, the slopes are 1 and 2, again unequal. In option D, both the slope and intercept are identical, so the equations represent the same line, not two distinct lines. Hence option A is the only pair satisfying both stated conditions.