Question 936805
given:

{{{x}}}|{{{-2}}}|{{{ 0}}}| ? |{{{ 7}}}
{{{y}}}|{{{-18}}}|  ? |{{{12}}}|{{{27}}}

to find missing numbers in a table, we need find equation first

{{{y=mx+b}}} where {{{m}}} is a slope and {{{b}}} is y-intercept
 
use two ordered pairs to find a slope: {{{x[1]=-2}}},{{{x[2]=7}}}, {{{y[1]=-18}}}, and {{{y[2]=27}}}

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}

{{{m=(27-(-18))/(7-(-2))}}}

{{{m=(27+18)/(7+2)}}}

{{{m=45/9}}}

{{{m=5}}}

so far we have {{{y=5x+b}}}


lets now use the Point-Slope formula to find the equation of the line

{{{y-y[1]=5(x-x[1])}}}

plug in  {{{x[1]=-2}}} and {{{y[1]=-18}}} 

{{{y-(-18)=5(x-(-2))}}}

{{{y+18=5(x+2)}}}

{{{y+18=5x+10}}}

{{{y=5x+10-18}}}

{{{y=5x-8}}}

now we can complete the table:


{{{x}}}|{{{-2}}}|{{{ 0}}}| {{{4}}} |{{{ 7}}}
{{{y}}}|{{{-18}}}| {{{ -8}}} |{{{12}}}|{{{27}}}

{{{y=5*0-8}}}=>{{{y=-8}}}
{{{12=5x-8}}}=>{{{5x=20}}}=>{{{x=4}}}


see the graph of this line and all points on it:

{{{drawing( 600, 600, -35, 35, -35, 35,circle(7,27,.35),circle(4,12,.35),circle(0,-8,.35),circle(-2,-18,.35),
locate(7,27,p(7,27)),locate(4,12,p(4,12)),locate(0,-8,p(0,-8)),locate(-2,-18,p(-2,-18)),
 graph( 600, 600, -35, 35, -35, 35, 5x-8)) }}}