Question 1003267

given:

Two lines are perpendicular: means their slopes are negative reciprocals to each other
if the slope of line 1 is {{{m}}}, then the slope of line 2 is {{{m[p]=-1/m}}}


Line 1 through ({{{-4}}},{{{ 1}}}) and ({{{-2}}},{{{ -3}}}): 
find the slope-intercept form of the equation or {{{y = mx + b}}} for this line using given points

*[invoke change_this_name10094 -4, 1, -2, -3]

so, your line 1 has equation {{{y=-2x-7}}}, and its slope is {{{m=-2}}}

now find negative reciprocal {{{m[p]=-1/m}}}

{{{m[p]=-1/-2}}}

{{{m[p]=1/2}}}

so far the equation of line 2 is {{{y=(1/2)x+b}}}

since given that Line 2 through ({{{2}}},{{{ 1}}}) =({{{x}}},{{{ y}}}), use this point to find {{{b}}} 

{{{1=(1/2)2+b}}}

{{{1=1+b}}}

{{{b=1-1}}}

{{{b=0}}}

now we have the equation of line 2: {{{y=(1/2)x+0}}} or {{{y=(1/2)x}}}


see them on a graph:

{{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,1,.12),locate(2,1,p(2,1)),
circle(-4,1,.12),locate(-4,1,p(-4,1)),
circle(-2,-3,.12),locate(-2,-3,p(-2,-3)),
 graph( 600, 600, -10, 10, -10, 10, -2x-7, (1/2)x)) }}}