What is the equation of the line that contains the points with (x,y) coordinates (–3,7) and (5,–1) ?

Answer 1

first you find the slope using formulae:
m = (y2-y1)/(x2-x1)
m = (-1-7)/(5+3)
m = -8/8
m = -1

then you substitute this into the formulae:
y = mx + b
y = -x + b (use one of the coordinates to find b)
7 = -(-3) + b
7 = 3 + b
7 - 3 = b
b = 4 (substitute back into the equation)

y = -x + 4 (there goes your answer!)

Answer 2

you would use point-slope form. the equation will be

1) y - 7 = - 4 (x - 3)

an other equation will be

2) y + 1 = - 4 (x - 5)

if you want standard form which the formula is A x + B y = C

1) 4 x + y = -5

2) 4 x + y = -19

to me i might have done some careless mistake, but i think the answer will be right.

Answer 3

y = -x + 4

Answer 4

y = mx + b

m = (y2 - y1)/(x2 - x1)

y2 = -1
y1 = 7

x2 = 5
x1 = -3

m = [(-1-7) / (5-(-3)] = (-8) / -8 = -1

y = -1x + b

7 = -1(-3) + b

7 = 3 + b
b = 4

y = -x + 4