How do you explain why two graphed lines have the same slopes but different y-intercepts?
-The lines are parallel.
-The lines are intersecting.
-The lines overlap completely.
-Not enough information is given.
The correct answer is: The lines are parallel.
When two graphed lines have the same slopes but different y-intercepts, it means that the lines have the same steepness but are shifted up or down on the y-axis. This indicates that the lines will never intersect, no matter how far they get extended. Therefore, the lines are parallel.
The correct explanation is: The lines are parallel.
When two graphed lines have the same slopes but different y-intercepts, it means they have the same steepness or rate of change but start at different points on the y-axis. This indicates that the lines are parallel.
To explain why two graphed lines have the same slopes but different y-intercepts, we can first understand that the slope of a line represents its steepness or incline, whereas the y-intercept is the point where the line intersects the y-axis.
If two lines have the same slope but different y-intercepts, the lines are parallel. Parallel lines never intersect, as they maintain the same distance between each other at all points along their length. This means that no matter how far you extend the lines, they will never cross or intersect.
To determine if two lines have the same slope, you can compare the coefficients of the x term in their equations. For example, if the equations of two lines are y = mx + b1 and y = mx + b2, where m represents the slope and b1 and b2 represent the y-intercepts, if the slopes 'm' are the same, it means the lines have the same steepness.
However, the different y-intercepts indicate that the lines are positioned at different heights vertically on the coordinate plane. They may have different starting points or different y-values when x is zero.
Therefore, in this case, since the lines have the same slopes but different y-intercepts, they are parallel to each other.