Question

A line passes through (2, –1) and (8, 4).Write an equation for the line in point-slope form.Rewrite the equation in standard form using integers.

Answer 1

Point Slope Form of a Line: y - y₁ = m(x - x₁)

Slope Formula:

   y₂ - y₁          4 - (-1)          5                             The slope is 5/6.
------------- = -------------- = ------
   x₂ - x₁          8 - 2              6

(2, -1) & (8,4) 
 x₁  y₁     x₂  y₂

Using all of the information above...
 
              
y + 1 = 5/6(x - 2) is your equation in point slope form.


Steps for rewriting this equation in standard form: 

Standard Form of a linear equation: ax + by = c 

1). Put the equation from PS form into Slope Intercept Form, which is y=mx+b

y + 1 = 5/6(x - 2)
 y + 1 = 5/6x - 5/3
    - 1               - 1
 ------------------------
 y = 5/6x - 8/3

2). Put the equation from Slope Intercept Form into Standard Form.

                     y  =   5/6x    - 8/3 
               - 5/6x    - 5/6x
            ______________________
              (-1) -5/6x + y(-1) = -8/3(-1)
           
                    5/6x - y = 8/3

The equation in standard form is 5/6x - y = 8/3.

I hope this helps you!