Question

Part 1: When writing linear equations, how do you determine which form of a line to use?

Part 2: Choose 1 set of points from the choices below. Then, solve the problem and post your solution, showing your steps.
Write an equation in point-slope form for the line that passes through one of the following pairs of points (you may choose the pair you want to work with). Then, use the same set of points to write the equation in standard form and again in slope-intercept form.

Point pairs
(5, 1), (–3, 4)
(0, –2), (3, 2)
(–2, –1), (1, 2)

Answer 1

It does not matter to me what form.
However if they give me two points like
(5, 1), (–3, 4)
, I am likely to do the following:
(y-1)/(x-5) = (4-1)/(-3-5)
(y-1)/(x-5) = (3)/(-8)
-8(y-1) = 3 (x-5)
-8y + 8 = 3 x -15
-8 y = 3 x -23
y = -(3/8) x + 23/8
which is in slope intercept form
but I could have done this:
m = (4-1)/(-3-5) = -3/8
so y = -(3/8) x + b
1 = -(3/8)5 + b
1 = -15/8 + b
b = 8/8+15/8 = 23/8
so
y = -(3/8) x + 23/8
which is remarkably similar to what I got the first way.
of course I could write that as
8 y = -3 x + 23
or
3 x + 8 y = 23
or whatever