Question

How do you write an equation of a line through the points (2,5) and (6,13) in standard form?

Answer 1

In general, given two points `(x_1,y_1)` and `(x_2,y_2)` we can equate two expressions for the slope, one involving variables `x` ans `y` and one determined solely by the given points:

`(y-5)/(x-5) = (13-5)/(6-2)`

`y-5 = 2(x-5)`

`y-5 = 2x -10`

Standard form for a line equation is
`Ax+By = C`

So we re-write our equation as
`2x-y = 5`