How do you explain why two graphed lines have the same slopes but different y-intercepts?
The lines overlap completely.
Not enough information is given.
The lines are parallel.
The lines are intersecting.
The lines are parallel.
The lines have the same slopes but different y-intercepts because they are parallel. The slope of a line represents its steepness, or how quickly it rises or falls as you move along the x-axis. When two lines have the same slope, it means they have the same steepness. However, the y-intercept represents the point at which the line crosses the y-axis. Since the y-intercepts are different, it means that even though the lines have the same steepness, they start at different points on the y-axis. As a result, the lines are parallel and will never intersect, no matter how far they are extended.
When two graphed lines have the same slopes but different y-intercepts, we can explain why by considering the equation of a line in slope-intercept form, which is y = mx + b. In this equation, "m" represents the slope of the line, and "b" represents the y-intercept, which is the point where the line crosses the y-axis.
If two lines have the same slope but different y-intercepts, it means that they have the same steepness or inclination. However, the difference in y-intercepts means that the lines are shifted vertically along the y-axis. This vertical shift causes the lines to have different starting points on the y-axis.
To determine if the lines are parallel, intersecting, or overlapping completely, we need to compare the slopes of the lines. If the slopes are the same and the y-intercepts are different, then the lines are parallel. Parallel lines never intersect and maintain the same distance apart from each other throughout their entire length.
If the lines do intersect at a single point, it means they have different slopes, even if the slopes are extremely close. Therefore, if the lines are intersecting, it would contradict the given information that they have the same slopes.
If the lines overlap completely, it means they are identical and coincide with each other at every point. Both the slopes and y-intercepts must be the same in this case. However, overlapping lines are not distinct and are essentially the same line, so it does not maintain different y-intercepts.
Based on the given information that the lines have the same slopes but different y-intercepts and they overlap completely, we can conclude that either not enough information is given or there may be an inconsistency or contradiction in the problem statement.