Question

How do you write an equation in standard form for a line passing through (2,9) and (1,3)?

Answer 1

Given two points `(x_1,y_1)` and `(x_2,y_2)`
The slope can be calculated as
`m= (y_1-y_2)/(x_1-x_2)`
For the points given `(2,9)` and `(1,3)`
this gives `m= 6`

We can then use this slope plus either one of the given points (I'm going to use `(1,3)` but it shouldn't make any difference)
to write the equation in slope-point form
`y-y_2 = m(x-x_2)`
or for our values
`y-3 = 6(x-1)`

Standard form for a line is
`Ax+By=C`
so we shift some values around to get

`(-6)x+(1)y = -3`