write an equation in point slope form for the line through the given points or through the given point with the given point slope

Question

(0,5), (-3,2)

Answer 1

First let's determine the slope

 

y₂ - y₁         2-5        -3

-------   =    -----   = ---  =  1

x₂ - x₁        -3-0        -3

 

Now the point slope equation of a line looks like

 

y-y₁ = m(x-x₁), where m = slope calculated above.

 

y-5 = 1(x-0)

 

Distributing and rearranging terms

y-5 = x, or

y = x + 5

Answer 2

Point-slope Form of the equation of a line is:

    y – y₁= m(x – x₁)                [ where (x₁,y₁) us a point on the line; m=slope of the line]

 

The problem gives 2 points, so we must computer the slope (that is, "rise over run") m:

      m = (y₂-y₁)/(x₂-x₁)

      m = ( 2-5 ) / ( (-3)-0 )

      m = (-3)/(-3)

      m = 1 

      

 Now, put P₁ and m into the point-slope formula:

     y - 5 = (1)(x - 0)       [this is the answer in point-slope form]