Question

What is the slope-intercept form of the line passing through `(2, 2)` and `(-1, 4)`?

Answer 1

`-2/3` is the slope and `10/3` is the intercept.

Explanation:

A line in the plane follow the equation

`y=mx+q`. In this equation we want to calculate the two parameters `m` and `q`. To do it we substitute the values of `x` and `y` and we have a system of equations

`2=2m+q`
`4=-1m+q`

from one of the two equation (for example the first) I write one variable as the other:

`2=2m+q` then `q=2-2m`

and now substitute this in the other equation

`4=-m+q` then `4=-m+2-2m`
`4=2-3m`
`4-2=-3m`
`2=-3m`
`m=-2/3`

to find `q` I take the `q=2-2m` and substitute the value of `m`

`q=2-2(-2/3)=2+4/3=10/3`

The line has equation

`y=-2/3x+10/3` where `-2/3` is the slope and `10/3` is the intercept.