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What is the slope of any line perpendicular to the line passing through #(13,-7)# and #(5,-2)#?

Answer 1

#=8/5#

Slope of the line passing through two given points #m=(-7+2)/(13-5)=-5/8# So the slope of the perpendicular to this one is #=-1/m=8/5#

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Answer 2

Eva Abramson

To find the slope of the line passing through the points (13, -7) and (5, -2), first calculate the slope using the formula:

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

Using the coordinates of the given points:

[ m = \frac{-2 - (-7)}{5 - 13} ] [ m = \frac{-2 + 7}{5 - 13} ] [ m = \frac{5}{-8} ] [ m = -\frac{5}{8} ]

The slope of the line passing through (13, -7) and (5, -2) is (-\frac{5}{8}).

To find the slope of any line perpendicular to this line, take the negative reciprocal of the slope:

[ m_{\perp} = -\frac{1}{m} = -\left(-\frac{8}{5}\right) = \frac{8}{5} ]

So, the slope of any line perpendicular to the line passing through (13, -7) and (5, -2) is (\frac{8}{5}).

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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.