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

3 Answers
Jan 28, 2017

Answer:

Slope is 5

Explanation:

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#

Jan 28, 2017

Answer:

#m=5#

Explanation:

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")#

Jan 28, 2017

Answer:

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.

Explanation:

#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#