<h2>
Point-Slope Form</h2>
Point-slope form is a form of a linear equation: ![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
is a point that falls on the line- <em>m</em> is the slope of the line
To write an equation in point-slope form:
- Calculate the slope of the line by solving for <em>m</em>
- Plug <em>m</em> into the general equation
- Plug a point that falls on the line in the general equation as
![(x_1,y_1)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29)
<h2>Solving the Question</h2>
We're given:
- The line passes through the points (f,g) and (h,j)
Solve for the slope (<em>m</em>):
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
⇒ Plug in the point (f,g) as (x,y):
![g-y_1=m(f-x_1)](https://tex.z-dn.net/?f=g-y_1%3Dm%28f-x_1%29)
⇒ Plug in the point (h,j) as (x₁,y₁):
![g-j=m(f-h)](https://tex.z-dn.net/?f=g-j%3Dm%28f-h%29)
⇒ Isolate <em>m</em> by dividing both sides by (f-h):
![\dfrac{g-j}{f-h}=m](https://tex.z-dn.net/?f=%5Cdfrac%7Bg-j%7D%7Bf-h%7D%3Dm)
⇒ <em>Therefore, the slope of the line is </em>
.
Plug the slope into the general equation:
![y-y_1=\dfrac{g-j}{f-h}(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3D%5Cdfrac%7Bg-j%7D%7Bf-h%7D%28x-x_1%29)
Plug one of the points, (f,g) or (h,j) into the equation as (x₁,y₁):
![y-j=\dfrac{g-j}{f-h}(x-h)](https://tex.z-dn.net/?f=y-j%3D%5Cdfrac%7Bg-j%7D%7Bf-h%7D%28x-h%29)
<h2>Answer</h2>
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=\dfrac{g-j}{f-h}(x-h)](https://tex.z-dn.net/?f=y-j%3D%5Cdfrac%7Bg-j%7D%7Bf-h%7D%28x-h%29)