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Question 443624: Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2 Please show all of your work.
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! 9 y = 7 x + 2 0.75
Divide by 9
y = 7/9 x 0.22
Compare this equation with y=mx+b
slope m = 0.78
The slope of a line perpendicular to the above line will be the negative reciprocal -1.29
m1*m2=-1
The slope of the required line will be -1.29
-1.29=-1.29
m= -1.29 ,point (-7,6)
Find b by plugging the values of m & the point in
y=mx+b
6=9.00+ b
b= -3
m= -1.29
The required equation is y=-1.29x-3
Answer by ikleyn(53430)  (Show Source):
You can put this solution on YOUR website! .
Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2
Please show all of your work.
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Strictly saying, the solution and the answer in the post by @mananth are incorrect.
Indeed, if I substitute coordinates (-7,6) into his equation y = -1.29x-3,
I will get y = -1.29*(-7) + 6 = 6.03, but not precisely 6,
which means that the point (-7,6) does not lie on the line.
In this my post, I will present a correct precise solution and the correct answer, and then will explain,
WHY the solution by @mananth is wrong.
Any line perpendicular to the given line -7x + 9y = -2 has an equation of the form
7y + 9x = c (1)
where 'c' is some real constant. So, we only need to find the value of 'c'.
To do it, we substitute the coordinates of the given point (-7,6) into equation (1)
7*6 + 9*(-7) = 42 - 63 = -21.
So, the sough equation is
7y + 9x = -21.
It is NOT that equation, which is presented as the answer in the post by @mananth.
So, I solved the problem correctly, and my answer is different from that by @mananth.
The error made by @mananth, is that he replaced the precise value m1 =  of the slope
of the original line by the decimal value 0.78.
This value, 0.78, is only approximation, but not the precise rational value.
So, the error by @mananth is that he uses his computer code in the form, which IS NOT APPLICABLE
and IS NOT ADEQUATE to the problem.
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