# How do you determine if the lines through the given points (4,6), (5,3) are parallel and which, if any, are perpendicular?

Please see the explanation.

In general, a line is parallel to another line, if the two lines have the same slope:

A line will be perpendicular to another line if the slope, n of the perpendicular line has the following relationship to the slope, m:

The slope of a line between the two points is:

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To determine if the lines through the given points (4,6) and (5,3) are parallel, we compare their slopes. If the slopes are equal, the lines are parallel. The slope formula is (y2 - y1) / (x2 - x1). For the given points, the slope of the first line is (3 - 6) / (5 - 4) = -3. The slope of the second line is undefined because (x2 - x1) is 0, indicating a vertical line. Therefore, the lines are not parallel. To determine if they are perpendicular, we check if the product of their slopes is -1. Since one slope is -3 and the other is undefined, their product is also undefined, meaning they are not perpendicular either.

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