Quickly Solve Algebra Equation: y-\frac{9}{2}=\frac{16}{15}(x-4) for Homework

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SUMMARY

The discussion centers on solving the algebraic equation y - 9/2 = 16/15(x - 4) and identifying errors in the solution process. The user initially misinterprets the problem as a linear equation but later realizes it involves derivatives for tangent and normal lines. The correct slope for the normal line is -16/15, derived from the negative reciprocal of the slope 16/15. This critical sign error led to confusion in reaching the final answer, which should be 32x + 30y = 263.

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  • Learn how to find tangent and normal lines to curves
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Students studying algebra and calculus, particularly those struggling with derivatives and their applications in finding tangent and normal lines.

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Homework Statement


y-\frac{9}{2}=\frac{16}{15}(x-4)

Homework Equations


y = mx+b?

The Attempt at a Solution



y-\frac{9}{2}=\frac{16}{15}(x-4)

15y-\frac{135}{2} = 16(x-4)

15y-\frac{135}{2} = 16x-64

30y-135=32x-128

30y-32x=7

The book says the answer is 32x + 30y = 263, which I can't get because of the negative sign. So either my algebra sucks, the given answer is wrong, or my original equation isn't right, but it should be since I'm given the points (4,\frac{9}{2}) and the slope is \frac{16}{15}.
 
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Looks right, what was the original question?
 
Oh yup, I screwed up the equation. The original question is a derivative where I had to figure out the equations for the tangent and normals of a line. I got 15/16 for slope and to get the normal, I just inverted it to get 16/15, when a normal is actually -1/slope which makes it -16/15. So that one wrong sign messed everything up. I was doubting my algebra...

Anyways thanks a lot :D
 

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