Question

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

Answer 1

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

`y = (1)x-12`

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

This can easily be achieved using the slope-point form of the equation: `(y-y_1) = m(x-x_1)`

In this case `y_1= (-5)`, `x_1=2`, and `m=1`

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