# Thread: straight line

1. ## straight line

Figure shows a straight line graph of log10y against log10x.

Given y=x^2n/k where n and k are constants.Calculate the value of n and k.

2. Originally Posted by mastermin346
Figure shows a straight line graph of log10y against log10x.

Given y=x^2n/k where n and k are constants.Calculate the value of n and k.
hi

$\displaystyle y=\frac{x^{2n}}{k}$

$\displaystyle \lg y=\lg {\frac{x^{2n}}{k}}$

$\displaystyle \lg y=2n\lg x-\lg k$

from the graph , we can see that the gradient is 1/2

so 2n=1/2 , n=1/4

- lg k =-1

lg k=1

k=??

3. Originally Posted by mathaddict
hi

$\displaystyle y=\frac{x^{2n}}{k}$

$\displaystyle \lg y=\lg {\frac{x^{2n}}{k}}$

$\displaystyle \lg y=2n\lg x-\lg k$

from the graph , we can see that the gradient is 1/2

so 2n=1/2 , n=1/4

- lg k =-1

lg k=1

k=??
how u get -logk=-1??

4. Originally Posted by mastermin346
how u get -logk=-1??
-log k is the y-intercept

5. Originally Posted by mastermin346
how u get -logk=-1??

owh..at point (o,-1), thanks a lot