Question

Write an equation in point-slope form for the line that passes through the points (f, g) and (h,j).

Answer 1

Point-Slope Form

Point-slope form is a form of a linear equation:
`y-y_1=m(x-x_1)`

• 
  `(x_1,y_1)` is a point that falls on the line
• m is the slope of the line

To write an equation in point-slope form:

1. Calculate the slope of the line by solving for m
2. Plug m into the general equation
3. Plug a point that falls on the line in the general equation as
   `(x_1,y_1)`

Solving the Question

We're given:

• The line passes through the points (f,g) and (h,j)

Solve for the slope (m):

`y-y_1=m(x-x_1)`

⇒ Plug in the point (f,g) as (x,y):

`g-y_1=m(f-x_1)`

⇒ Plug in the point (h,j) as (x₁,y₁):

`g-j=m(f-h)`

⇒ Isolate m by dividing both sides by (f-h):

`(g-j)/(f-h)=m`

⇒ Therefore, the slope of the line is
`(g-j)/(f-h)`.

Plug the slope into the general equation:

`y-y_1=(g-j)/(f-h)(x-x_1)`

Plug one of the points, (f,g) or (h,j) into the equation as (x₁,y₁):

`y-j=(g-j)/(f-h)(x-h)`

Answer

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):

`y-j=(g-j)/(f-h)(x-h)`