# How do you write equations of a line parallel to x - y - 12 = 0 that passes through (2, -5)?

Apr 9, 2015

Re-write the equation $x - y - 12 = 0$ into a slope-intercept form $y = m x + b$

$y = \left(1\right) x - 12$

So we are looking for line with slope of $1$ through the point $\left(2 , - 5\right)$

This can easily be achieved using the slope-point form of the equation: $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

In this case ${y}_{1} = \left(- 5\right)$, ${x}_{1} = 2$, and $m = 1$

So our equation is
$y + 5 = \left(1\right) \left(x - 2\right)$
which simplifies as
$y = x - 7$