Question

What is the equation of the line passing through `(21,185)` and `(111,-32)`?

Answer 1

`90y = -217x +21207`

Explanation:

The general formula for a line is `y= mx +c` where `m` is the slope and `c` is the `y` intercept. By substituting the coordinates of the two points given we can solve for `m` and `c`.
`185 = m*21 +c`
`-32 = m*111 +c`
Subtract the second equation form the first and get
`185+32 = 21m -111m`
`217 = -90m`
`m = - 217/90`
Plug this into the first equation to find `c`
`185 = -217/90*21 +c`
`c = (185*90 +217*21)/90`
`c=(16650+4557)/90`
`c = 21207/90`
The equation is therefore `y = -217x/90 +21207/90`
or `90y = -217x +21207`