Question 916844
*[invoke change_this_name10094 5, 11, -3, 7] 

if lines are parallel, they have same slope; 

{{{0.5}}} will be a slope of the line through (-2,k) and (2,5)

{{{y=0.5x+b}}}

use (2,5) to find {{{b}}}


{{{5=0.5*2+b}}}

{{{5=1+b}}}

{{{b=5-1}}}

{{{b=4}}}


now we have: {{{y=0.5x+4}}}

use (-2,k) to find {{{k}}}

{{{k=0.5(-2)+4}}}

{{{k=-1+4}}}

{{{k=3}}}

so, {{{y=0.5x +8.5}}} is parallel to {{{y=0.5x+4}}}

 {{{drawing( 600, 600, -10, 10, -10, 15,locate(2,5,p(2,5)),locate(-2,3,p(-2,3)),locate(-3,7,p(-3,7)),locate(5,11,p(5,11)),circle(5,11,.2),circle(-3,7,.2),circle(2,5,.2),circle(-2,3,.2), graph( 600, 600, -10, 10, -10, 15, 0.5x+8.5, 0.5x+4) )}}}