Question 666499: Write a linear equation to fit the following data(linear regression)
1)Through (7,12) with m = -4/5
2) Perpendicular to 3x-4y=8 and through (-1,1)
3) Parallel to 3x-4y=8 and through (-1,1)
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! m= - 4/5
Plug value of the slope and point(7, 12 ) in
Y = m x + b
12 = - 4/5 * 7 + b
12 = -5 3/5 + b
b= 12 + 28/5
b= 88/ 5
So the equation will be
Y = - 4/5 x + 88/5
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3 x -4 y = 8
Find the slope of this line
-4 y = -3 x + 8
Divide by -4
y = 3/ 4 x + -2
Compare this equation with y=mx+b, m= slope & b= y intercept
slope m = 3/4
The slope of a line perpendicular to the above line will be the negative reciprocal -4/3
Because m1*m2 =-1
The slope of the required line will be -4/3
m= -4/3 ,point ( -1 , 1 )
Find b by plugging the values of m & the point in
y=mx+b
1 = 4/ 3 + b
b= - 1/3
m= -1 1/3
The required equation is y= -4/ 3 x - 1/ 3
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PARALLEL
3 x -4 y = 8
Find the slope of this line
make y the subject
-4 y = -3 x + 8
Divide by -4
y = 3/4 x -2
Compare this equation with y=mx+b
slope m = 3/4
The slope of a line parallel to the above line will be the same
The slope of the required line will be 3/4
m= 3/4 ,point ( -1 , 1 )
Find b by plugging the values of m & the point in
y=mx+b
1 = - 3/ 4 + b
b= 1.75
m= 3/4
Plug value of the slope and b in y = mx +b
The required equation is y = 3/4 x + 7/ 4
m.ananth@hotmail.ca
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