How do you explain why two graphed lines have the same slopes but different y-intercepts?
(1 point)
• The lines are intersecting.
• The lines are parallel.
The lines overlap
completely.
Not enough information is
given.
The correct answer is: The lines are parallel.
Are you sure
Yes, I am sure. When two lines have the same slope but different y-intercepts, it means that they are parallel. This is because the slope determines the steepness of the line, while the y-intercept represents the point at which the line intersects the y-axis. So, even though the lines have the same slope, they start at different points on the y-axis, which makes them parallel and never intersect.
A line has an equation of
y = -X + 6. What are the slope
and y-intercept? (1 point)
O The slope is 1, and the y-intercept is 6.
o The slope is 6, and the y-
intercept is -1.
The slope is -1, and the
y-intercept is 6.
O There is no slope, and the
y-intercept is 6.
The correct answer is: The slope is -1, and the y-intercept is 6.
If two graphed lines have the same slopes but different y-intercepts, it means that the lines are parallel. The fact that they have the same slopes indicates that they have the same steepness or inclination, but their different y-intercepts means that they are not intersecting at any point. If the lines were intersecting, they would have different slopes. Furthermore, the lines overlapping completely is not possible since they are parallel and never meet. Therefore, the correct explanation is that the lines are parallel.
To explain why two graphed lines have the same slopes but different y-intercepts, we can observe the equation of a straight line, which is typically represented by y = mx + b, where m is the slope and b is the y-intercept.
When two lines have the same slope, it indicates that they have the same steepness or inclination. This means that for every unit increase in the x-coordinate, both lines will increase or decrease by the same amount in the y-coordinate.
However, the difference in the y-intercepts means that the lines start at different points on the y-axis. The y-intercept represents the value of y when x is zero. Hence, two lines with different y-intercepts have different starting points on the y-axis even though their slopes are equal.
Based on this explanation, we can conclude that the lines are not intersecting or overlapping since they have different y-intercepts. It is also not possible to determine whether the lines are parallel, intersecting, or overlapping solely based on the information provided.