Question

, find the slope of Line 1 and Line 2, then explain if the lines are parallel, perpendicular, or neither.

Line 1: (3, 2) and (1, 4)
Line 2: (6, 1) and (4, 3)

Answer 1

The slopes of Line 1 and Line 2 are both -1, indicating that the lines are parallel since they have identical slopes.

Step-by-step explanation:

To find the slope of Line 1 and Line 2, we use the formula for slope which is (change in y) / (change in x), often represented as (y2 - y1) / (x2 - x1).

For Line 1, with points (3, 2) and (1, 4), the slope can be calculated as:

Slope of Line 1 = (4 - 2) / (1 - 3) = 2 / -2 = -1

For Line 2, with points (6, 1) and (4, 3), the slope is:

Slope of Line 2 = (3 - 1) / (4 - 6) = 2 / -2 = -1

Since both lines have identical slopes, this means Line 1 and Line 2 are parallel to each other, as parallel lines have the same slope.

To determine if lines are perpendicular, we would look for slopes that are negative reciprocals of each other, but that is not the case here.