How do you explain why two graphed lines have the same slopes but different y-intercepts?
the lines overlap completely.
the lines are parallel.
the lines are intersecting.
not enough information is given.
If two graphed lines have the same slopes but different y-intercepts, it means that both lines have the same steepness or inclination, but they start at different points on the y-axis.
1. If the lines overlap completely, it means they have the same equation and represent the same line.
2. If the lines are parallel, it means they have the same slope and will never intersect.
3. If the lines are intersecting, it means they have the same slope, but different y-intercepts, and they intersect at a specific point.
4. If not enough information is given, it means we cannot determine if the lines are parallel, intersecting, or overlapping solely based on the information provided.
so whats the answer
The correct answer would be "not enough information is given" since we cannot determine the relationship between the lines based solely on the information given.
a line has an equation of y= - x + 6. what are the slope and y-intercept?
the slope is 1, and the y-intercept is 6.
the slope is 6, and the y-intercept is -1
there is no slope, and the y-intercept is 6
the slope is -1, 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, they are parallel. The reason for this is that the slope of a line represents its steepness or inclination, while the y-intercept is the point where the line intersects the y-axis.
When two lines have the same slope, it means that they have the same steepness, which indicates that they are moving in the same direction. However, since they have different y-intercepts, it means that they do not intersect and remain at a constant distance from each other. Therefore, the lines are parallel.
When two graphed lines have the same slopes but different y-intercepts, they are considered as parallel lines. Here's the explanation:
To determine the slope of a line given its equation, we can use the formula: slope = (change in y) / (change in x). If the slopes of two lines are equal, it means that for every unit change in x, there is an identical change in y. Therefore, the lines have the same steepness or incline.
However, the y-intercept represents the point where the line intersects the y-axis. It is the value of y when x = 0. Since the y-intercepts are different, the lines have different starting points on the y-axis, even though their slopes are the same.
Here's an example to visualize this: Consider two lines with the equations y = 2x + 3 and y = 2x + 1. Both lines have a slope of 2 because for every unit increase in x, the corresponding y-value increases by 2. However, the first line intersects the y-axis at y = 3, while the second line intersects it at y = 1. Thus, the lines are parallel since they have the same slope but different y-intercepts.
In summary, when two graphed lines have the same slopes but different y-intercepts, they are parallel lines.