Question

Consider the relationship (y+3)2 = b/(x-2), where y and x are variables and bis a constant. On rectangular coordinate paper, what is the slope of a graph of In(y+3) on the vertical axis versus In(x-2) on the horizontal axis?

Answer 1

Answer:

(-1) is the slope of a graph of In(y+3) on the vertical axis versus In(x-2) on the horizontal axis.

Explanation:

$\frac{(y+3)}{2} = \frac{b}{(x-2)}$

Taking natural logarithm on both the sides:

$\ln [(y+3)]-\ln[2]=\ln [b]-\ln [(x-2)]$

$\ln [(y+3)]=\ln[2]+\ln [b]-\ln [(x-2)]$

$\ln [(y+3)]=\ln {[2\times b]-\ln [(x-2)]$

Slope intercept form is generally given as:

$y=mx+c$

m = slope, c  = intercept on y axis or vertical axis

On rearranging equation:

$\ln [(y+3)]=(-1)\times \ln [(x-2)]+\ln {2b}$

y = ln [(y+3)], x = ln [(x-2)], m=-1 , c  = ln 2b

(-1) is the slope of a graph of In(y+3) on the vertical axis versus In(x-2) on the horizontal axis.