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What is the slope of any line perpendicular to the line passing through #(-3,-12)# and #(5,-3)#?

Answer 1

#-8/9#

A line perpendicular to another line has an OPPOSITE RECIPROCAL slope.

For example, if a line had a slope of #2#, the perpendicular line's slope would be #-1/2#. Similarly, a line with slope #-3/5# would be perpendicularly intersected by a line with a slope of #5/3#.

To find the slope of the perpendicular line, first find the slope of the original line.

#"slope"=(y_2-y_1)/(x_2-x_1)#

#=(-3-(-12))/(5-(-3))=(-3+12)/(5+3)=9/8#

The perpendicular line's slope will be the opposite reciprocal of #9/8#, which is #-8/9#.

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Answer 2

Nathan Axel

To find the slope of the line passing through (-3, -12) and (5, -3), first calculate the slope using the formula ( m = \frac{{y_2 - y_1}}{{x_2 - x_1}} ). Then, determine the negative reciprocal of this slope to find the slope of any line perpendicular to it.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.