Find the equation of the line perpendicular to y=-x-2 and passing through the point (4, 1).

\( k: y=m_1x+b_1;\ l: y=m_2x+b_2\\\\k\ \perp\ l\iff m_1m_2=-1\\====\\k: y=-x-2;\ l: y=mx+b\\\\k\ \perp\ l\iff-1\cdot m=-1\Rightarrow m=1\\\\l: y=1x+b\to y=x+b\\\\(4;\ 1)\to substitute\ x=4\ and\ y=1\ to\ y=x+b:\\\\4+b=1\\b=1-4\\b=-3\\\\Answer: y=x-3 \)

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First, you need to remember that perpendicular lines have negative reciprocal slopes.

The given line has slope of -1, so the line perpendicular to it has slope of +1/1 = 1.

So the equation of the new line is going to be [  y = 1x + intercept  ].

You know that the new line goes through the point where x=4 and y=1.
Stick these into the part of the equation that you already know:

y = 1x + intercept

1 = 1(4) + intercept.

Can you find the intercept from here?
Maybe I’d better just finish it off.

1 = 4 + intercept.

Subtract 4 from each side:

intercept = -3

So the equation of the line perpendicular to [  y = -x - 2  ]  going through (4, 1) is

y = x - 3


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