Writing Equations of Lines?

Question

1) Write the equation of the line with a slope of -1/3 and passing through the point (6, -4).
2) Write the equation of the line passing through the points
(-6,1) and (-4,2).

Answer 1

1)
Use coordinates as a test point.

y = mx + b

-4 = (-1/3)(6) + b
-4 = -2 + b
b = -2

y = -(1/3)x - 2

2)
slope = rise / run
m = ( y2 - y1 ) / ( x2 - x1 )
m = ( 2 - 1 ) / ( -4 - (-6) ) = 1/2

m = mx + b
2 = (1/2)(-4) + b
b = 4

y = (1/2)x + 4

Answer 2

1) -1/3 = y+4/ x-6
3y + 12= -x +6
3y = -x - 6
y = -1/3x - 3

2) 2-1/ -4+6 = 1/2
1/2 = y-2/ x+4
2y - 4 = x +4
2y = x +8
y = 1/2x +4

Answer 3

Point- slope form is:
y-y1 = m(x-x1), where m = slope and (x1,y1) is the point.

Two-point form is:
(y-y1)/(x-x2) = (y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are the two points.