Question: Equations of lines, passing though (perpendicular & parallel to) (-1,5) 2x+4y=1? Is this correct...\n\ny-5=1/2(x-(-1))\ny=1/2x+2\ny=1/2x+3/2 (parallel)\n\ny-5=-2(x-5)\ny=-2x+5 (perpendicular)\n\nThank you!

Answer: First we put the equation\n2x+4y=1\ninto slope-intercept form.\n\n4y = -2x + 1\ny = -1/2x + 1/4\nThe slope is -1/2.\n\nThen using point-slope form, we find parallel equation through (-1,5): x1 is -1 and y1 is 5\n(y-y1) = m(x-x1)\ny-5 = -1/2(x--1)\ny-5 = -1/2(x+1)\ny-5 = -1/2x - 1/2\ny-10/2 = -1/2x - 1/2\ny = -1/2x + 9/2\n\nThen using point-slope form, we find perpendicular equation through (-1,5) with slope 2.  To get the perpendicular slope, you take the negative reciprocal.  Again, x1 is -1 and y1 is 5.\n(y-y1) = m(x-x1)\ny-5 = 2(x--1)\ny-5 = 2(x+1)\ny-5 = 2x + 2\ny = 2x + 7
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