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

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Answer 1 · 2015-04-09T19:14:48

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

$y = (1) x - 12$ $y = (1)x-12$

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

This can easily be achieved using the slope-point form of the equation: $(y - y_{1}) = m (x - x_{1})$ $(y-y_1) = m(x-x_1)$

In this case $y_{1} = (- 5)$ $y_1= (-5)$ , $x_{1} = 2$ $x_1=2$ , and $m = 1$ $m=1$

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

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