Answers:
1. AB: y = - 2x - 6
2. BC: y = x - 3
3. CD: x = 3
4. AD: y = (3/7) x +26/7
Solution:
y-y1=m(x-x1)
m=(y2-y1)/(x2-x1)
1. AB
A=(-4,2)=(xa, ya)→xa=-4, ya=2
B=(-1,-4)=(xb, yb)→xb=-1, yb=-4
mab=(yb-ya)/(xb-xa)
mab=(-4-2)/(-1-(-4))
mab=(-6)/(-1+4)
mab=(-6)/(3)
mab=-2
y-ya=mab (x-xa)
y-2=-2(x-(-4))
y-2=-2(x+4)
y-2=-2x-8
y-2+2=-2x-8+2
y=-2x-6
2. BC
B=(-1,-4)=(xb, yb)→xb=-1, yb=-4
C=(3,0)=(xc, yc)→xc=3, yc=0
mbc=(yc-yb)/(xc-xb)
mbc=(0-(-4))/(3-(-1))
mbc=(0+4)/(3+1)
mbc=(4)/(4)
mbc=1
y-yc=mbc (x-xc)
y-0=1 (x-3)
y=x-3
3. CD
C=(3,0)=(xc, yc)→xc=3, yc=0
D=(3,5)=(xd, yd)→xd=3, yd=5
mcd=(yd-yc)/(xd-xc)
mcd=(-4-0)/(3-3)
mcd=(-4)/(0)
mcd= Infinite (Vertical line)
Equation vertical line: x=xc=xd
x=3
4. AD
A=(-4,2)=(xa, ya)→xa=-4, ya=2
D=(3,5)=(xd, yd)→xd=3, yd=5
mad=(yd-ya)/(xd-xa)
mad=(5-2)/(3-(-4))
mad=(3)/(3+4)
mad=3/7
y-ya=mad (x-xa)
y-2=(3/7)(x-(-4))
y-2=(3/7)(x+4)
y-2=(3/7)x+12/7
y-2+2=(3/7)x+12/7+2
y=(3/7)x+(12+7(2))/7
y=(3/7)x+(12+14)/7
y=(3/7)x+26/7