# Linear Law

• Apr 17th 2010, 06:12 AM
Punch
Linear Law
http://i952.photobucket.com/albums/a...g/P4170010.jpg

My attempt at manipulating the equation

$y^2=e^{ax+4}$
$2lny=(-ax+4)lne$
$lny=\frac{(-ax+4)}{2}$
$lny=\frac{-a}{2}x+2$
• Apr 17th 2010, 07:54 AM
Quote:

Originally Posted by Punch
http://i952.photobucket.com/albums/a...g/P4170010.jpg

My attempt at manipulating the equation

$y^2=e^{ax+4}$
$2lny=(-ax+4)lne$
$lny=\frac{(-ax+4)}{2}$
$lny=\frac{-a}{2}x+2$

hi

gradient $=-\frac{a}{2}=\frac{-4-b}{2}$ -- equation 1

the y-intercept is 2 , so we know another point (0,2)

gradient $=-\frac{a}{2}=\frac{b-2}{2}$ -- equation 2

so now you hv 2 equations , whats next ?
• Apr 17th 2010, 07:54 AM
running-gag
You are right

Using the point (4,-4) gives you the value for a
$-4 = -\frac{a}{2} \times 4 + 2$

Then using the point (2,b) gives you the value for b
• Apr 17th 2010, 05:47 PM
Punch
From $lny=\frac{-a}{2}x+2$, substituting the point (4,-4)

I would have to take $lny=ln(-4)$ which shows error 2 in the calculator.
confused
• Apr 17th 2010, 09:41 PM
Quote:

Originally Posted by Punch
From $lny=\frac{-a}{2}x+2$, substituting the point (4,-4)

I would have to take $lny=ln(-4)$ which shows error 2 in the calculator.
confused

ln y (the whole thing) is -4 not the y inside the ln .
• Apr 18th 2010, 12:58 AM
Punch
Oh... This means, $lny=\frac{-a}{2}x+2$ is expressed as Y=mX+C where where Y is the y coordinate and X is the x-coordinate
• Apr 18th 2010, 03:46 AM
Oh... This means, $lny=\frac{-a}{2}x+2$ is expressed as Y=mX+C where where Y is the y coordinate and X is the x-coordinate