Question 177233
<pre>
Kindly help me with the following sum regarding 
linear relation and explain please:
Find the missing y coordinate values in the 
following table:

 x |  y
-2 | -6
-1 |  ?
 0 |  ?
 1 | 18
<font size = 4 color = "indigo"><b>
First we find the equation of the line that goes through
the two point for which we are given both coordinates, 
that is, the points {{{matrix(1,1,"(-2,-6)")}}} and {{{matrix(1,1,"(1,18)")}}}

{{{drawing(200,800,-4,3,-8,20, graph(200,800,-4,3,-8,20,8x+10),  locate(-2-.12,-6+.34,o),locate(-2,-6,"(-2,-6)"),
locate(1-.14,18+.34,o), locate(1,18,"(1,18)")

 )}}}


We first find the slope using the slope formula:

{{{matrix(1,5,m,"","=","",(y[2]-y[1])/(x[2]-x[1])) }}} 

{{{matrix(1,5,m,"","=","",((18)-(-6))/((1)-(-2))) }}}

{{{matrix(1,5,m,"","=","",(18+6)/(1+2)) }}}

{{{matrix(1,5,m,"","=","",24/3) }}}

{{{matrix(1,5,m,"","=","",8) }}}

Then we use the point-slope formula for the equation
of a line:

{{{matrix(1,3,y-y[1],"=",m(x-x[1])) )}}}

{{{matrix(1,3,y-(-6),"=",(8)(x-(-2)) )}}}

{{{matrix(1,3,y+6,"=",8(x+2))}}}

{{{matrix(1,3,y+6,"=",8x+16)}}}

{{{matrix(1,3,y,"=",8x+10)}}}

Now we find the missing points in the chart:

 x |  y
-2 | -6
-1 |  ?
 0 |  ?
 1 | 18

by substituting -1 for x,

{{{matrix(1,3,y,"=",8x+10)}}}
{{{matrix(1,3,y,"=",8(-1)+10)}}}
{{{matrix(1,3,y,"=",-8+10)}}}
{{{matrix(1,3,y,"=",2)}}}

and by substituting 0 for x

{{{matrix(1,3,y,"=",8x+10)}}}
{{{matrix(1,3,y,"=",8(0)+10)}}}
{{{matrix(1,3,y,"=",0+10)}}}
{{{matrix(1,3,y,"=",10)}}}

So we fill in the missing
values for y:

 x |  y
-2 | -6
-1 |  2
 0 | 10
 1 | 18

And as we see the points
(-1,2) and (0,10) lie right on the same line as two
points (-2,-6) and (1,18).

{{{drawing(200,800,-4,3,-8,20, graph(200,800,-4,3,-8,20,8x+10),  locate(-2-.12,-6+.34,o),locate(-2,-6,"(-2,-6)"),
locate(1-.14,18+.34,o), locate(1,18,"(1,18)"),
locate(-1-.14,2+.34,o),locate(-3,2.5,"(-1,2)"),locate(0-.14,10+.34,o),
locate(0,10,"(0,10)") 
 )}}} 

Edwin</pre>