(-2,4) and (10,8)

Question

What is the point-slope form?

(-2,4) and (10,8)

Answer 1

The "point slope form" is:  y-y₁= m(x-x₁)

Where (x₁,y₁) is a point on the graph and m is the slope.

 

First find the slope between the

two points (-2,4), (10,8)

m = (y₂-y₁)/(x₂-x₁) = (8-4)/(10-(-2)) = 4/12 = 1/3

 

Your slope is m= 1/3

 

For point slope form use either given point for (x₁,y₁)

and 1/3 for the slope m in the equation

y-y₁ = m(x-x₁)

Let's use (-2,4)

 

y-4 = (1/3)(x-(-2))

y-4 = (1/3)(x+2)

 

This is the point slope form of the line.

 

 

Answer 2

Two points determine a line.  Here are two points:  (-2,4) and (10,8)

 

The point-slope form of the equation of a line is:

     (y - y₁) = ( (y₂ - y₁) / (x₂ - x₁) ) (x - x₁)

 

     (y - 4) = ( (8 - 4) / (10 - (-2)) ) (x - (-2))

     (y - 4) = ( 4/12) (x + 2)

     (y - 4) = (1/3)(x + 2)             [point-slope form]

                     [slope is (1/3); we used point (-2,4)]