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

No…these lines are parallel
No…these lines are parallel

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

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

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

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

No…these lines are perpendicular

Answer 1

To determine if the lines through the two sets of points intersect, we need to examine the slopes of the lines represented by each set of points.

1. Calculate the slope for each set of points: The slope (m) can be calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).

2. Once the slopes are calculated:

   • If the slopes are equal, the lines are parallel and do not intersect.
   • If the slopes are negative reciprocals (multiply to -1), the lines are perpendicular and intersect at a right angle.
   • If the slopes are neither equal nor negative reciprocals, the lines are not parallel nor perpendicular and will intersect at some point.

Since the actual data points for the tables are not provided in your question, I cannot directly calculate the slopes or make a definitive conclusion. However, without the specific values, you cannot determine the relationship between the lines (whether they intersect or not).

Based on the options provided, the best response would be:

You cannot tell without a graph.

If you have the specific points from the tables, I could help calculate the slopes to provide a more definitive answer!