Final answer:
The slope of a line is a measure of its steepness. To determine if lines are parallel, perpendicular, oblique, or coinciding, we compare their slopes.
Step-by-step explanation:
The slope of a line is a measure of its steepness. To find the slope of each line, we need to determine the change in y-coordinates divided by the change in x-coordinates between any two points on the line. If the slopes are the same, then the lines are parallel; if the slopes are opposite reciprocals, then the lines are perpendicular; if the slopes are different, then the lines are oblique; and if the lines are the same line, then they are coinciding.
In case A, since the lines are parallel to each other and are along the x-axis, their slopes will be the same, so they are parallel.
In case B, since the lines are mutually perpendicular to each other, their slopes will be opposite reciprocals, so they are perpendicular.
In case C, the lines have different slopes, so they are oblique.
In case D, the lines are the same line, so they are coinciding.