How do you explain why two graphed lines have the same slopes but different y -intercepts?(1 point) Responses
The lines overlap completely.
The lines overlap completely.
Not enough information is given.
Not enough information is given.
The lines are intersecting.
The lines are intersecting.
The lines are parallel.
The lines are parallel.
The lines are parallel.
To explain why two graphed lines have the same slopes but different y-intercepts, it is important to understand their definitions and how they relate to the graphs.
The slope of a line represents the steepness or incline of the line. It can be calculated by finding the ratio of the vertical change (change in y-value) to the horizontal change (change in x-value) between two points on the line.
On the other hand, the y-intercept of a line is the point where the line intersects the y-axis. It represents the value of y when x is equal to zero.
Now, if two lines have the same slopes but different y-intercepts, it means that they have the same rate of change but start at different points on the y-axis.
One way to determine this is by using the slope-intercept form of a linear equation, which is y = mx + b. Here, m represents the slope, and b represents the y-intercept.
For example, if we have two lines:
Line 1: y = 2x + 3
Line 2: y = 2x - 2
Both lines have a slope of 2, indicating the same rate of change. However, Line 1 has a y-intercept of 3, while Line 2 has a y-intercept of -2.
To visualize this on a graph, plot the points where the lines intersect the y-axis. Line 1 will intersect at (0, 3), and Line 2 will intersect at (0, -2). Notice that even though the lines have different starting points, they still have the same slope.
Therefore, the correct explanation is: The lines have the same slopes but different y-intercepts.