SOLUTION: whats the slope of the coordinates M (9,6), N(1,4) and whats the slope perpendicular to it

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Question 475578: whats the slope of the coordinates M (9,6), N(1,4) and whats the slope perpendicular to it
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: is the first point . So this means that x%5B1%5D=9 and y%5B1%5D=6.
Also, is the second point . So this means that x%5B2%5D=1 and y%5B2%5D=4.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%284-6%29%2F%281-9%29 Plug in y%5B2%5D=4, y%5B1%5D=6, x%5B2%5D=1, and x%5B1%5D=9


m=%28-2%29%2F%281-9%29 Subtract 6 from 4 to get -2


m=%28-2%29%2F%28-8%29 Subtract 9 from 1 to get -8


m=1%2F4 Reduce


So the slope of the line that goes through the points and is m=1%2F4



The slope of any line perpendicular to this one will have a slope that is a negative reciprocal of this one. So simply flip the fraction and change the sign to get -4%2F1=-4


So the perpendicular slope is -4

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the slope


Slope of the line through the points (9, 6) and (1, 4)



m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%284+-+6%29%2F%281+-+9%29


m+=+%28-2%29%2F%28-8%29


m+=+1%2F4



Answer: Slope is m+=+1%2F4



the slope perpendicular to it is m=-1%281%2F4%29=-4

now we can find the Equation of a line that passes through M (9,6) and N(1,4)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (9,6) and (1,4)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (9,6) and (x%5B2%5D,y%5B2%5D) is the second point (1,4))


m=%284-6%29%2F%281-9%29 Plug in y%5B2%5D=4,y%5B1%5D=6,x%5B2%5D=1,x%5B1%5D=9 (these are the coordinates of given points)


m=+-2%2F-8 Subtract the terms in the numerator 4-6 to get -2. Subtract the terms in the denominator 1-9 to get -8




m=1%2F4 Reduce



So the slope is

m=1%2F4





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-6=%281%2F4%29%28x-9%29 Plug in m=1%2F4, x%5B1%5D=9, and y%5B1%5D=6 (these values are given)



y-6=%281%2F4%29x%2B%281%2F4%29%28-9%29 Distribute 1%2F4


y-6=%281%2F4%29x-9%2F4 Multiply 1%2F4 and -9 to get -9%2F4

y=%281%2F4%29x-9%2F4%2B6 Add 6 to both sides to isolate y


y=%281%2F4%29x%2B15%2F4 Combine like terms -9%2F4 and 6 to get 15%2F4 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (9,6) and (1,4) is:y=%281%2F4%29x%2B15%2F4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F4 and the y-intercept is b=15%2F4


Notice if we graph the equation y=%281%2F4%29x%2B15%2F4 and plot the points (9,6) and (1,4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F4%29x%2B15%2F4 through the points (9,6) and (1,4)


Notice how the two points lie on the line. This graphically verifies our answer.




y=%281%2F4%29x%2B15%2F4
so, the line perpendicular to it is y=-4x%2B15%2F4
+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F4%29x%2B15%2F4%2C+-4x%2B15%2F4%29+