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

[iamsmooth]

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 $\frac{16}{15}$.

 

[Pengwuino]

Looks right, what was the original question?

 

[iamsmooth]

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