Question 956035
A(-5, 4) B(3, -3) and C(5, -2)



A(-5, 4) B(3, -3)...find equation of the line passing through

{{{m=(y[2]-y[1])/(x[2]-x[1])=(-3-4)/(3-(-5))=-7/8}}}

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

{{{y-4=(-7/8)(x-(-5))}}}

{{{y-4=-(7/8)(x+5)}}}

{{{y=-(7/8)x-(7/8)5+4}}}

{{{y=-(7/8)x-35/8+32/8}}}

{{{y=-(7/8)x-3/8}}}



B(3, -3) and C(5, -2)

...find equation of the line passing through

{{{m=(y[2]-y[1])/(x[2]-x[1])=(-2-(-3))/(5-3)=(-2+3)/2=1/2}}}

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

{{{y-(-3)=(1/2)(x-3)}}}

{{{y+3=(1/2)(x-3)}}}

{{{y=(1/2)x-3/2-3}}}

{{{y=(1/2)x-9/2}}}


A(-5, 4) and C(5, -2)

...find equation of the line passing through

{{{m=(y[2]-y[1])/(x[2]-x[1])=(-2-4)/(5-(-5))=-6/10=-3/5}}}

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

{{{y-4=-(3/5)(x-(-5))}}}

{{{y=-(3/5)(x+5)+4}}}

{{{y=-(3/5)x-(3/5)5+4}}}

{{{y=-(3/5)x-3+4}}}

{{{y=-(3/5)x+1}}}




{{{drawing(600, 600, -10, 10, -10, 10,triangle(-5, 4,3, -3,5, -2),
red(locate(-5,4,"A(-5,4)" ), locate(3,-3,"B(3,-3)"), locate(5,-2,"C(5,-2)")),
 graph( 600, 600, -10, 10, -10, 10, -(7/8)x-3/8,-(3/5)x+1,(1/2)x-9/2)) }}}