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 whether the lines through the two sets of points intersect, we need to assess the slopes of the lines formed by those points. However, since the tables with the points are not provided, I cannot calculate the slopes directly.

Here’s how you can figure it out if you have the data:

1. Calculate the slopes of the lines represented by the points in each table. The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated with the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

2. Compare the slopes:

   • If the slopes are the same, the lines are parallel and do not intersect.
   • If the slopes are negative reciprocals of each other (meaning their product equals -1), the lines are perpendicular and intersect at a right angle.
   • If the slopes are different (and not negative reciprocals), the lines are neither parallel nor perpendicular and will intersect at some point.

If you get the slopes to determine the relationship between the lines, you can answer accordingly.

Without the specific point values, the question "Does the line through the first set of points intersect with the line through the second set of points?" cannot be answered without additional information or the actual points to analyze.

In this case, the most accurate option based on the provided responses is: You cannot tell without a graph.