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

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The discussion revolves around solving the algebraic equation y - 9/2 = 16/15(x - 4). The user initially struggles with the algebraic manipulation and arrives at an incorrect form of the equation. Upon realizing a mistake in identifying the original problem as a derivative involving tangent and normal lines, they correct their understanding of the slope. The confusion stemmed from misapplying the concept of the normal line's slope. Ultimately, the user acknowledges the error and expresses gratitude for the clarification.
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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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