Given that the slope of a line is -1/5, what is the slope of a line that is perpendicular to it?

Answer 1

Slope is 5

The perpendicular to a given slope is its negative reciprocal. This means the fraction is flipped and multiplied by #-1#. So perpendicular to #-1/5# is #5#
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Answer 2

#m=5#

The perpendicular slope of any original slope is derived by negating the original slope and then "flipping" the fraction. By "flipping" the fraction, I mean find the inverse of the original slope. So for example:

Original slope: #m_("orig")=-1/5#

Step 1. Negate the original slope. Remember that a negative of a negative is a positive.

#-(-1/5)=1/5#

Step 2. "Flip" the fraction, finding it's inverse. Remember that whole numbers can be turned automatically into fractions by placing them over a 1.

#5/1=5=m_("perp")#

More generally, you can always find the perpendicular slope using this formula:

#m_("perp")=-1/m_("orig")#
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Answer 3

All you have to do is remember and follow the method in the first bit of the explanation.

The rest is supportive expansion and contains the actual solution.

#color(blue)("THE REALLY IMPORTANT BIT: The basic rule")#
Let the slope (gradient) of the first line be #m#
Then the gradient of the perpendicular line is #-1/m# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Comment")#

This s true for any straight or curved line graph.

The only difference is that for a straight line it is a constant value but for a curved line it changes to suit the gradient at each and every point

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("The calculation")# The given slope is #-1/5# which is a constant. Thus the graph is that of a straight line.
The gradient of the perpendicular is: #(-1)xx(-5/1) = +5/1# #" "color(red)(uarr)# #" "color(red)("Inverting the given gradient")# ................................................................................. #color(blue)("Foot note")#
I left the answer in the format of #5/1# as it represents a ratio.

For every 1 along you go up 5

The teacher will expect you to write the answer gradient as 5 and not #5/1#
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Answer 4

The slope of a line perpendicular to a line with slope m is the negative reciprocal of m. Therefore, if the slope of one line is -1/5, the slope of a line perpendicular to it is the negative reciprocal of -1/5, which is 5.

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Answer 5

The slope of a line perpendicular to a line with slope ( m ) is the negative reciprocal of ( m ).

So, if the slope of a line is ( -\frac{1}{5} ), the slope of a line perpendicular to it is ( \frac{5}{1} ) or simply ( 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.

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.

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.

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.

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