Question

How do you write the equation in point slope form given (0,-2) with slope = -3/7?

Answer 1

`y+2=m(x-0)" "larr` In full form

`y+2=mx" "larr` In simplified form

Explanation:

For any given point `P_i ->(x_i,y_i)" and gradient "m`

We have `y-y_i=m(x-x_i)`

In other words you are looking just at the gradiant.

There is no need to worry about the `c` in `y= mx + c` as it is implied and locked into the condition `y-y_i=m(x-x_i)`. You can only have one value for `c` to make `(x_i,y_i)` work.

So for your question we have:

Given that `P_i ->(x_i,y_i) ->(0,-2)`

`color(brown)( y-y_i=m(x-x_i))color(blue)(" "->" " y-(-2)_i=m(x-0) )`

`y+2=m(x-0)`