Question

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)ResponsesYes…these lines are parallelYes…these lines are parallelYes…these lines are perpendicularYes…these lines are perpendicularYou cannot tell without a graphYou cannot tell without a graphYes…these lines are not parallel nor perpendicularYes…these lines are not parallel nor perpendicularNo…these lines are perpendicularNo…these lines are perpendicularNo…these lines are parallel

Answer 1

In order to determine if the lines through the points in the two sets are parallel, perpendicular, or neither, we need to calculate the slopes of both lines.

1. Parallel lines have the same slope.
2. Perpendicular lines have slopes that are negative reciprocals of each other (i.e., if one slope is \( m \), the other slope must be \( -\frac{1}{m} \)).
3. If the slopes are neither the same nor negative reciprocals, then the lines are neither parallel nor perpendicular.

Let’s denote the first set of points as \( (x_1, y_1) \) and \( (x_2, y_2) \), and the second set of points as \( (x_3, y_3) \) and \( (x_4, y_4) \).

The formula for the slope of a line through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

You will need to find the slopes of both lines using their respective points, and based on the values:

• If the slopes are equal, choose "Yes…these lines are parallel."
• If the slopes are negative reciprocals, choose "Yes…these lines are perpendicular."
• If neither condition is satisfied, choose "Yes…these lines are not parallel nor perpendicular."

Since the actual table of points has not been provided, it is impossible to definitively answer the question without knowing the specific points. If you supply the coordinates, I can help you calculate the slopes and derive the correct conclusion.