Both of these tables represent linear graphs:

Question

Does the line through the first set of points intersect with the line through the second set of points?

(1 point)
Responses

Yes…these lines are not parallel nor perpendicular
Yes…these lines are not parallel nor perpendicular

No…these lines are perpendicular
No…these lines are perpendicular

You cannot tell without a graph
You cannot tell without a graph

Yes…these lines are parallel
Yes…these lines are parallel

Yes…these lines are perpendicular
Yes…these lines are perpendicular

No…these lines are parallel

Answer 1

To determine if the lines through two sets of points intersect, we need to evaluate both lines based on their equations and slopes.

A line's equation can be expressed in the slope-intercept form $y=mx+b$, where $m$ represents the slope. If two lines have the same slope ($m$), they are parallel and will not intersect unless they are the same line (in which case they have infinitely many points of intersection). If they have slopes that are negative reciprocals of each other (i.e., $m_1\cdot m_2=-1$), they are perpendicular.

Since you have not provided the actual data points for the two sets of points, I can't calculate their slopes and ascertain the relationship between the lines directly.

If you could provide the coordinates or data for both sets of points, I will be able to tell if the lines intersect or not. Otherwise, based solely on the options you have given, it's not possible to determine the intersection without additional information (hence, "You cannot tell without a graph" seems valid).