how to put this in slope intercept and standard form

Question

(2,-3 )( -2,5)

Answer 1

Hi Diamond!

1st step -- grab the slope= "rise over the run"= y rises from -3 to 5 or 8 slots ... x runs backward from 2 to -2 or -4 slots ... slope is 8/-4 or m= -2 ... ... negative "tilt" makes sense, since (2,-3) is in SE zone and (-2,5) is in NW part of grid ... 

2nd step -- find the intercept ... try y(x)= -2x  with (-2,5) ,,, y(-2)= -2(-2) is 4, which is 1 slot short of 5 ... add +1 to  boost the y(x)

Answer ==> y(x) = -2x + 1 ... check using (2,-3) ... y(2)= -2(2) + 1= -4+1= -3 :)  Best wishes ... 

Answer 2

1. y = mx + b  - slope-intercept form linear equation
2. Ax + By = C  - standard form of linear equation (A ≥ 0)
3. y - y₁ = m(x - x₂) - two-point form
            y₁ - y₂      
4. m = ————  
            x₁ - x₂    

4.   (x₁ , y₁)     (x₂ , y₂)  
      (2 , -3)      (-2 , 5)

       -3 - 5           -8          -8  
m = ———— =  ——— = —— = – 2
       2 - (-2)       2 + 2        4 

(3. ---> 1.)  y – y₁ = –2(x – x₁)
    y - (-3) = -2(x - 2) ---> y + 3 = -2x + 4 ---> y = -2x + 1

2. y = - 2x + 1 ---> 2x + y = 1