Question 1203671
  Find {{{ C }}} such that ({{{ 10}}} ,{{{ -1}}} ), ({{{ -4}}} ,{{{ 10}}} ), and ({{{ C}}} ,{{{ -6}}} ) lie on a line. What is the {{{ C}}}  value?


the slope of the line can be calculated using the slope formula:


{{{ m=(y2-y1)/(x2-x1)}}} 

{{{ m=(10-(-1))/(-4-10)}}} 

{{{ m=(10+1)/(-14)}}} 

{{{ m=-11/14}}} 


We know that the slope between the two points ({{{ 10}}} ,{{{ -1}}} ) and  ({{{ C}}} ,{{{ -6}}} ) is also equal to {{{ -11/14}}} 
 

 that is, we can set up an equation involving {{{ C}}}  and solve for {{{ C}}} 


{{{ (-6-(-1))/(C-10)=-11/14}}} 

{{{ (-6+1)/(C-10)=-11/14}}} 

{{{ -5/(C-10)=-11/14}}} 

{{{ -5*14=-11(C-10)}}} 

{{{-70=-11C+110}}} 

{{{ 11C=70+110}}} 

{{{ C=180/11}}} 


answer is:

 {{{ C = 180/11}}} 


and the point is:

({{{ 180/11}}} ,{{{ -6}}} )