Question

Find the equation of the line through the point (-1/2,-2) and parallel to the line 4x + y = -4.  Write your answer in general form.  Do not use any space between the letter (lower case), symbol and number, say x+y-1=0

Answer 1

y=-4x-4 is another way to write the equation of the line. All lines parallel have the same gradient so y=-4x+a where a is a constant is a way of writing the equation of a parallel line so we have to find a by plugging in the point: -2=-4(-½)+a, -2=2+a, so a=-4 and the equation of the parallel line is y=-4x-4 which is the original line! So the point lies on the original line and 4x+y=-4, 4x+y+4=0 in general form.