Determine whether the lines passing through the following points are perpendicular, parallel, or neither.
Line 1: (1,4) and (-2,5)
Line 2: (5,-2) (3,4)
Explain your reasoning

Parallel lines have the same slope. Perpendicular lines have slopes which are negative reciprocals. Neither would be slopes without either relationship. To determine the relationship, calculate the slope between each pair of points using the slope formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}= \frac{5-4}{-2-1}=-\frac{1}{3}[/tex]

[tex]m = \frac{y_2-y_1}{x_2-x_1}= \frac{4--2}{3-5}=\frac{6}{-2}=-3[/tex]

Since the slopes are reciprocals but the same sign, this is neither.

Determine whether the lines passing through the following points are perpendicular, parallel, or neither. Line 1: (1,4) and (-2,5) Line 2: (5,-2) (3,4) Explain your reasoning ​

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Determine whether the lines passing through the following points are perpendicular, parallel, or neither.
Line 1: (1,4) and (-2,5)
Line 2: (5,-2) (3,4)
Explain your reasoning