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write an equation of the line that is:
 
  a) parallel to the line y=4x+1, and that passes through point (2,3)
  b) parallel to the line 2y-6x=9, and that passes through point (-2,1)
  c) parallel to the line y=4x+3, and that has the same y-intercept as the line y=5x-3
  d) parallel to the line -1/2x, and that has the same y-intercept as the line 2y=7x+6
  e) perpendiclar to the line 2y-4x=8, and that passes through point (6,-6)
  f) perpendicular to the line 2y-5x=15, and has an x-intercept of  3

  please help me with all the questions it would mean alot

Sagot :

Luanaidn
[tex]a)\\y=4x+1\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\substituting\point\ (2,3)\\3=4*2+c\\c=-5\\y=4x-5\\b)\\2y-6x=9\\2y=6x+9\\y=3x+4,5\\a=3\\new\ y=bx+c\\if\ parallel a=b\\y=3x+c\\substituting\ point\ (-2,1)\\1=4*(-2)+c\\c=9\\y=3x+9\\ c)\\y=4x+3\\a=4\\new\ y=bx+c\\if\ parallel a=b\\y=4x+c\\c=-3\\y=4x-3\\e)\\2y-4x=8\\2y=4x+8\\y=2x+4\\a= 2 \\new\y=bx+c\\if\ perpendicular b=-1/a\\y=- \frac{1}{2} x+c\\point(6,-6)\\-6=-1/2*6+c\\c=-3\\y=-1/2x-3\\f)\\2y-5x=15\\2y=5x+15\\y=\frac{5}{2}x+\frac{15}{2}[/tex]
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