Question 1155614


a. Find the slope of the line, L1, that goes through the points 

({{{ 4}}}, {{{-3}}}) and ( {{{2}}}, {{{2}}}).

the slope of the line is: 

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

{{{m=(2-(-3))/(2-4)}}}

{{{m=(2+3)/(-2)}}}

{{{m=-5/2}}}


b. Write the equation of the line, L1. Write in slope intercept form.

{{{y=mx+b}}}

plug in a slope and coordinates of one point, ( {{{2}}}, {{{2}}})

{{{2=-(5/2)2+b}}}........solve for {{{b}}}

{{{2=-5+b}}}

{{{2+5=b}}}

{{{b=7}}}

=> equation is:{{{y=-(5/2)x+7}}}




c. Find the slope of the line, L2, that is perpendicular to L1.

perpendicular lines have slopes negative reciprocal to each other

if the slope of the line L1 is {{{-5/2}}}, the slope of the line L2 will be

 {{{m=-1/(-5/2)=2/5}}}

d. Write the equation of the line, L2, that goes through the point ( {{{-3}}}, {{{5}}} ).

{{{y=(2/5)x+b}}}........plug in given point

{{{5=(2/5)(-3)+b}}}

{{{5=-6/5+b}}}

{{{b=6.2}}}


=> equation is:{{{y=(2/5)x+6.2}}}



{{{drawing( 600, 600, -10, 10, -10, 10, 
circle(2,2,.12),locate(2,2,p(2,2)),
circle(4,-3,.12),locate(4,-3,p(4,-3)),circle(-3,5,.12),locate(-3,5,p(-3,52)),
 graph( 600, 600, -10, 10, -10, 10,(2/5)x+6.2 ,-(5/2)x+7)) }}}