What this in point slop form : (-3,2) and (5,-2)

Question

Please help me find this 

Answer 1

slope:  m = (change in y)/(change in x)

m = (-2-2)/(5-(-3)) = -4/8 = -1/2

 

Point slope:  y - y₁ = m(x-x₁) 

where m is slope and (x₁, y₁) is on the line.

Let's use (-3, 2) as (x₁, y₁)

 

y - 2 = (-1/2)(x-(-3))

y - 2 = (-1/2)(x + 3).  

This is an equation of the line in point slope format.

                    

You could also use (5, -2) as (x₁, y₁)

y - (-2) = (-1/2)(x - 5)

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

 

Both answers are correct.  If you change them

to standard form, ax + by = c, they will be equal.

 

Look at first equation.

y - 2 = (-1/2)(x+3)

2(y-2) = -(x+3)

2y - 4 = -x - 3

x + 2y = 1

 

Look at second equation.

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

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

2y + 4 = -x + 5

x + 2y = 1

 

As you can see, they are the same.