Question

write the standard form of the equations:
through (1,3) and (-4, -4)

through (5,4) and parallel to y=4

Answer 1

1. (1,3), (-4,-4).

Slope = (-4-3)/(-4-1) = -7/-5 = 7/5.
y = mx + b = 3.
(7/5)*1 + b = 3
7/5 + b = 3
b = 15/5 - 7/5 = 8/5.
Y = (7/5)x + 8/5.
Multiply both sides by 5:
5y = 7x + 8
STD Form: 7x - 5y = -8.

Another Method.
1. (1,3), (-4,-4).
Slope = (-4-3)/(-4-1) = -7/-5 = 7/5.

(1,3),(x,y). m = 7/5.
m = (y-3)/(x-1) = 7/5.
Cross multiply:
7x-7 = 5y-15
STD Form:7x - 5y = -8.

2. (5,4), Y = 4.
Y = 4 is a hor. line, and it is 4 units
above the x-axis. Y = 4 for all values of x.

(5,4), (7,4).
Slope = (4-4)/(7-5) = 0/2 = 0.

We'll derive the Eq of a line that is 4 units below the x-axis.
(2,-4), (4,-4). m = 0.
Y = mx+b = -4.
0*2 + b = -4
b = -4.
Y = 0x + (-4)
Eq: Y = -4.