Question 1149757


given:

 an x-intercept of {{{3}}} =>({{{3}}},{{{0}}}) 

 a y-intercept of {{{k}}} =>({{{0}}},{{{k}}}) 

passes through a point ({{{5}}},{{{8}}}) 

Find: {{{k}}}

we have two points, so we can find slope: 

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}

{{{m=(8-0)/(5-3)}}}

{{{m=8/2}}}

{{{m=4}}}


use slope intercept formula:

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

{{{y=4x+k}}}.......use   point, ({{{3}}},{{{0}}}) 

{{{0=4*3+k}}}....solve for {{{k}}}

{{{0=12+k}}}

{{{k=-12}}}

then  y-intercept of {{{k}}} =>({{{0}}},{{{-12}}}) 

so, the line is:

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





{{{drawing( 600, 600, -10, 10, -10, 10,
circle(5,8,.12), 

locate(5,8,p(5,8)),

 graph( 600, 600, -10, 10, -10, 10, 4x-12)) }}}