Point-slope form is a form of a linear equation: [tex]y-y_1=m(x-x_1)[/tex]
To write an equation in point-slope form:
We're given:
Solve for the slope (m):
[tex]y-y_1=m(x-x_1)[/tex]
⇒ Plug in the point (f,g) as (x,y):
[tex]g-y_1=m(f-x_1)[/tex]
⇒ Plug in the point (h,j) as (x₁,y₁):
[tex]g-j=m(f-h)[/tex]
⇒ Isolate m by dividing both sides by (f-h):
[tex]\dfrac{g-j}{f-h}=m[/tex]
⇒ Therefore, the slope of the line is [tex]\dfrac{g-j}{f-h}[/tex].
Plug the slope into the general equation:
[tex]y-y_1=\dfrac{g-j}{f-h}(x-x_1)[/tex]
Plug one of the points, (f,g) or (h,j) into the equation as (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
There can be multiple answers for this question, depending on what we consider to be (x,y) and what we consider to be (x₁,y₁). This is one of the possible answers, for (f,g) is (x,y) and (h,j) is (x₁,y₁):
[tex]y-j=\dfrac{g-j}{f-h}(x-h)[/tex]
