find the equation of straight lines through the point (2,-1) and making angle of 45 degree with the perpendicular to one another.

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lfryerda | High School Teacher | (Level 2) Educator

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We can find the equation of a line that goes through `(2,-1)` with a slope of m by substituting into `y=mx+b` and solving for b.

This means we solve `-1=2m+b` and get `b=-1-2m`.

So the equation of a line with slope m is `y=mx-1-2m`.

If a line has an angle of 45 degrees to the horizontal, this is the same has having slope of m=1, so the first line has the equation `y=x-3` .

Two lines are perpendicular if their slopes are negative reciprocals, or `m_P=-1/m` .  That means that the slope of the second line has slope of `m_P=-1`.  Then the equation of the second line is `y=-x+1`.