Both of these tables represent linear graphs:
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 perpendicular
Yes…these lines are perpendicular
No…these lines are parallel
No…these lines are parallel
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
To determine if the line through the first set of points intersects with the line through the second set of points, we need to analyze the relationship between the lines.
If the lines are perpendicular, they will intersect at a right angle. To determine if this is the case, we need to find the slopes of the two lines. If the slopes are negative reciprocals of each other, the lines are perpendicular.
If the lines are parallel, they will never intersect and their slopes will be equal.
If the lines are neither parallel nor perpendicular, they may still intersect but at a different angle than perpendicular.
To make a definitive conclusion, we would need to see the graphs of the lines. So, without a graph, we cannot tell whether the two lines intersect or not.
To determine whether the lines represented by the two sets of points intersect or not, you can follow these steps:
1. Determine the equation of each line:
- For the first set of points, determine the equation of the line passing through those points.
- For the second set of points, determine the equation of the line passing through those points.
2. Compare the equations of the two lines to identify their relationship:
- If the slopes of the two lines are equal, and the y-intercepts are different, then the lines are parallel and do not intersect.
- If the slopes of the two lines are different, then the lines are not parallel, but they may or may not intersect.
- If the product of their slopes is -1, then the lines are perpendicular and will intersect.
3. Once you have determined the relationship between the lines based on their equations, you can select the appropriate response:
- If the slopes are equal and the y-intercepts are different, the lines are parallel.
- If the slopes are different, the lines are not parallel but may or may not intersect.
- If the slopes have a product of -1, the lines are perpendicular.
- If you cannot determine the relationship without a graph, select the option stating that you cannot tell without a graph.
By following these steps, you will be able to determine whether the lines represented by the two sets of points intersect or not.