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

Apr 3, 2015

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

If $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are two points on a line then the slope is given by
$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

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

$\frac{y - 7}{x - 0} = \frac{12 - 7}{\left(- 5\right) - 0}$

Simplifying we have
$y - 7 = \frac{5 x}{- 5}$
or
$y = 7 - x$

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