Question 1134565


Find an equation of the line that passes through ​({{{1}}}​,{{{2}}}​) and that is parallel to {{{y=3x+4}}}. 

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

if given that line is parallel to {{{y=3x+4}}}, than {{{m=3}}}; parallel lines have same slope

so far, your equation is {{{y=3x+b}}}

now use given point  ​({{{1}}}​,{{{2}}}​), plug in coordinates and calculate {{{b}}}


{{{2=3*1+b}}}

{{{2-3=b}}}

{{{b=-1}}}

and your equation is:

{{{highlight(y=3x-1)}}}


{{{drawing ( 600, 600, -10, 10, -10, 10,
circle(1,2,.12), locate(1,2,p(1,2)),
graph( 600, 600, -10, 10, -10, 10, 3x-1, 3x+4)) }}}