Question 1187696



  an equation of the line is: 

{{{y=mx+b}}}  where {{{m}}} is a slope and {{{b}}} is y-intercept

if the line   is parallel to the line {{{2y + x=3}}}, means the line will have same slope

find a slope of

{{{2y + x=3}}}......solve for {{{y}}}

{{{y =-x/2+3/2}}}=> slope {{{m=-1/2}}}

so far, equation is

{{{y=-(1/2)x+b}}}

 if the line passes through the midpoint of ({{{-2}}},{{{3}}})and ({{{5}}},{{{4}}}), we need to find midpoint {{{M}}}

{{{M}}}= ({{{(-2+5)/2}}},{{{(3+4)/2}}})= ({{{3/2}}},{{{7/2}}})

use midpoint to calculate {{{b}}}

{{{7/2=-(1/2)(3/2)+b}}}

{{{7/2=-(3/4)+b}}}

{{{7/2+3/4=b}}}

{{{b=17/4}}}

and your line is

{{{y=-(1/2)x+17/4}}}



{{{ drawing( 600, 600, -10, 10, -10, 10, 
circle(3/2,7/2,.12),locate(3/2,7/2,M(3/2,7/2)),
circle(-2,3,.12),locate(-2,3,p(-2,3)),
circle(5,4,.12),locate(5,4,p(5,4)),
green(line(-2,3,5,4)),
graph( 600, 600, -10, 10, -10, 10, -x/2+3/2, -(1/2)x+17/4) )}}}