Question 444813
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I need to find the equation of the line containing (-2, -7) and (-5, -8)
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        This problem requires an exact solution in the form of an equation expressed in rational numbers.

        But @mananth in his post works with decimal numbers with two decimals after the decimal point.

        It does not produces an exact equation in precise form.

        So, what he presents as a solution, is not a solution in precise strict meaning 

        and can not be accepted as a solution to the problem.


        Below I develop  EXACT  equation in the form as it  SHOULD  be done.



<pre>
Calculate the slope  m = {{{((-8)-(-7))/((-5)-(-2))}}} = {{{(-1)/(-3)}}} = {{{1/3}}} = 0.3333333...


So, an equation of the line in slope-intercept form is

    y = mx + b = {{{(1/3)x}}} + b.


We should determine the value of 'b' in this equation. 
For it, substitute coordinates of the either given point into the equation

    -7 = {{{(1/3)*(-2)}}} + b,

    -7 = {{{-2/3}}} + b,

    b = -7 + {{{2/3}}} = -6{{{1/3}}} = {{{-19/3}}}.


The exact equation is

    y = {{{(1/3)x - 19/3}}}.


At this point, the problem solved PRECISELY and CORRECTLY.
</pre>

Solved.


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I know &nbsp;(I just deciphered it out for myself some time ago) &nbsp;that solutions by @mananth 
are produced by the computer code.


Detecting this error &nbsp;(I just detected it for the second time) &nbsp;means that the computer code 
has a defect &nbsp;(= a hole), &nbsp;which should be fixed.