Question 28529: The line through points (m,-9) and (7,m) has a slope of m. What is the value of m?
Answer by sdmmadam@yahoo.com(530)   (Show Source):
You can put this solution on YOUR website! The line through points (m,-9) and (7,m) has a slope of m. What is the value of m?
The slope of a line joining two given points A(x1,y1) and B(x2,y2) is given by slope =(y2-y1)/(x2-x1) -----(1)
In the given problem we have A(X1,y1) given by A(m,-9) implying x1=m, y1=-9
and B(X2,y2) given by B(7,m) implying x2=7, y2=m
And given slope = m
Therefore using the formula (1), we have
m = [m-(-9)]/[7-m]
m(7-m) = (m+9) [multiplying through out by (7-m)]
7m-m^2 = m +9
0 = m^2-7m+m+9
(taking both the terms from the left to the right, change side then change sign)
That is 0 = m^2-6m+9
0= (m-3)^2
[as (m^2-6m+9) is a perfect square of the form a^2-2ab+b^2
where here a = m and b=3]
And (m-3)^2 = 0 implies m=3 (the equation has root 3 occurring twice)
Answer: m = 3
Verifiation: The points A(m,-9) and B(7,m) become
A(3,-9) and B(7,3)
and the slope of the line through A(3,-9) and B(7,3) by formula (1) is
[3-(-9)]/(7-3) = (3+9)/4 = 12/4 = 3 = m which is the given slope.
Hence our answer for m is right
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