Question 956468

Write the equation for the following relation.

C = {({{{x}}}, {{{y}}}): ({{{6}}}, {{{15}}}), ({{{8}}}, {{{21}}}), ({{{10}}}, {{{27}}}), . . .}

{{{y=mx +b}}}

we can first find a slope {{{m}}} using two given points ({{{6}}}, {{{15}}}) and  ({{{8}}}, {{{21}}})

{{{m=(21-15)/(8-6)=6/2=3}}}

{{{y=3x +b}}}

now use any of given points, substitute {{{x}}} and {{{y}}}, solve for {{{b}}}

  {{{y=3x +b}}}.....if {{{x=8}}} and {{{y=21}}}, we have

{{{21=3*8 +b}}}

{{{21=24 +b}}}

{{{21-24=b}}}

{{{b=-3}}}

so, your equation is: {{{highlight(y=3x-3)}}}

let check if all points lie in a line:

{{{drawing( 600, 600, -30, 30, -30, 30,
circle(6,15,.2),circle(8,21,.2),circle(10,27,.2),
locate(6,15,p(6,15)),locate(8,21,p(8,21)),locate(10,27,p(10,27)),
 graph( 600, 600, -30, 30, -30, 30, 3x-3)) }}}