Question 1125283
{{{S }}}|{{{   T}}}
{{{_ }}}|{{{   70}}}
{{{_}}}|{{{     66}}}
{{{9 }}}|{{{    62}}}
{{{12 }}}|{{{  58}}}
{{{15}}}|{{{    54}}}


first find equation using two of given pairs

{{{T=mS+b}}}...plug in {{{S=9 }}}|{{{   T= 62}}}

{{{62=9m+b}}}...solve for {{{b}}}

{{{b=62-9m}}}....eq.1


{{{T=mS+b}}}...plug in {{{S=12 }}}|{{{   T= 58}}}

{{{58=12m+b}}}...solve for {{{b}}}

{{{b=58-12m}}}....eq.2

since let sides of eq.1 and eq.2 are same, equal right sides


{{{62-9m=58-12m}}}.......solve or {{{m}}}

{{{12m-9m=58-62}}}

{{{3m=-4}}}

{{{m=-4/3}}}


now find {{{b}}}


{{{b=62-9m}}}....eq.1

{{{b=62-9(-4/3)}}}

{{{b=62-cross(9)3(-4/cross(3))}}}

{{{b=62-3(-4)}}}

{{{b=62+12}}}

{{{b=74}}}


so, your equation is: {{{T=-(4/3)S+74}}}


ind missing numbers in the table:

{{{S }}}|{{{   T}}}....->{{{70=-(4/3)S+74}}}->{{{(4/3)S=74-70}}}->{{{(4/3)S=4}}}->{{{S=4/(4/3)}}}->{{{S=3}}}
{{{3 }}}|{{{   70}}}
{{{6}}}|{{{     66}}}....->{{{66=-(4/3)S+74}}}->{{{(4/3)S=74-66}}}->{{{(4/3)S=8}}}->{{{S=8/(4/3)}}}->{{{S=6}}}
{{{9 }}}|{{{    62}}}
{{{12 }}}|{{{  58}}}
{{{15}}}|{{{    54}}}