Question 1204122




the slope-intercept equation of the function is:

{{{y=mx+b }}}

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


The graph of f passes through ({{{3}}}, {{{14}}}) 

{{{14=m(3)+b}}} 

{{{14=3m+b }}}


since our line is parallel  to the line that passes through ({{{10}}}, {{{2}}}) and ({{{25}}}, {{{15}}}), and we know parallel lines have same slope
, use given points of parallel line to find a slope

{{{m=(15-2)/(25-10)=13/15}}}


going back to 

{{{14=3m+b}}}  ....substitute slope

{{{14=3(13/15)+b }}}

{{{14=(13/5)+b }}}

{{{b=14-13/5}}}

{{{b=57/5}}}

now we have a slope and {{{y}}}-intercept, so our line is:

{{{y=(13/15)x+57/5}}}


{{{ drawing( 600, 600, -10, 15, -10, 15, 
circle(3,14,.12), locate(3,14,p(3,14)),
graph( 600, 600, -10, 15, -10, 15, (13/15)x+57/5)) }}}