Chemistry: 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?

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Consider the relationship (y+3)2 = b/(x-2), where

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03.01.2022

(-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.

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