Question

How do you write the equation of the line through the given points in standard form: (0,7) (-5,12)?

Answer 1

For a straight line the slope between any two points on the line is the same no matter which two point you choose.

If `(x_1,y_1)` and `(x_2,y_2)` are two points on a line then the slope is given by
`(y_2-y_1)/(x_2-x_1)`

Consider a general (variable) point on the desired line: `(x,y)` plus the two given points. Remembering that the slope is always equal no matter which two points you choose:

`(y-7)/(x-0) = (12-7)/((-5)-0)`

Simplifying we have
`y-7 = (5x)/(-5)`
or
`y = 7-x`

Depending upon your definition of "standard form" this might be expressed as
`x+y = 7`