Question 1131651


Write the equation of the line through 
({{{5}}}, {{{3}}})
 that is parallel to 
{{{4x + 5y = 12}}}

parallel lines have same slope; so, first write the equation of the given line in slope-intercept form


{{{4x + 5y = 12}}}


 {{{ 5y = -4x+12}}}

{{{ y = -(4/5)x+12/5}}}

{{{ y = -(4/5)x+2.4}}}

so, the slope is {{{-(4/5)}}}

and parallel line will be

{{{y=-(4/5)x+b}}}


use given point ({{{5}}}, {{{3}}}) to find {{{b}}}

{{{3=-(4/5)5+b}}}

{{{3=-(4/cross(5))cross(5)+b}}}

{{{3=-4+b}}}

  {{{3+4=b}}}

{{{b=7}}}

and the equation of the parallel line is

{{{y=-(4/5)x+7}}}



{{{drawing ( 600, 600, -10, 10, -10, 10, 
circle(5,3,.12), locate(5,3,p(5,3)),
graph( 600, 600, -10, 10, -10, 10, -(4/5)x+2.4, -(4/5)x+7)) }}}