Write the point slope form of an equation of the line that passes through the given point and has a given slope. (1;3), m=-2 (-6;3), m=-2/3

There are two basic forms of an equation of the line, the
point-slope and the standard form.
(the standard is sometimes also called the
slope-intercept
form). 

Standard:

y
= mx+n (1)

where m - the slope of the line and n - the
y-intercept (the value of y when
x=0)

Point-Slope:

(y-y1)
= m(x-x1) (2)

where m is the slope  and (x1,y1) is the
given point.

We'll substitute the first pair slope-given
point in (2):

Point slope: y - 3 = -2(x -
1)

We'll remove the
brackets:

y - 3 = -2x +
2

We'll put the equation in the standard form by adding 3
both sides:

y = -2x + 2 +
3

Standard: y = -2x +
5

We'll do the same thing with the next
given pair: (-6;3),
m=-2/3.

Point-Slope:
y - 3 = (-2/3)(x + 6)

We'll remove the
brackets:

 y - 3 = -2x/3 -
4

We'll add 3 both sides:

y =
-2x/3 - 4 + 3

y = -2x/3 -
1

Standard:
y = -2x/3 - 1