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 perpendicular
No…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 perpendicular
Yes…these lines are perpendicular

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

No…these lines are parallel
No…these lines are parallel
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page 5 of 5

Answer 1

To determine whether the lines represented by the given tables intersect, we need to calculate the slopes of both lines.

1. Identify the slope of each line: The slope \( m \) for a linear graph can be calculated using the formula:

   \[ m = \frac{y2 - y1}{x2 - x1} \]

   If we have two points from each table, we can calculate the slopes.

2. Compare the slopes:

   • If the slopes are equal, the lines are parallel and do not intersect.
   • If the slopes are different, the lines are not parallel and do intersect.
   • If the slopes are negative reciprocals (i.e., their product is -1), then the lines are perpendicular. They will intersect at exactly one point.

3. Conclusion:

   • If you know the points from both tables, plug them into the slope formula to compare their slopes.
   • If the slopes are equal, then the answer is “No…these lines are parallel.”
   • If the slopes are different, the answer is “Yes…these lines are not parallel nor perpendicular.”
   • If the slopes are negative reciprocals, the answer is “Yes…these lines are perpendicular.”

Since you did not provide the actual data from the tables, I cannot calculate specific slope values, but this is how you would determine whether the lines intersect. If you provide the points, I can help with the calculations!