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write an equation of the line that is:

   a) parallel to the line y=2x-4, and has a y-intercept of 7
   b) parallel to the line y-3x=6, and has a y-intercept of -2
   c) parallel to the line 2x+3y=12, and that passes through the origin
   d) perpendicular to the line y=3x+2, and has a y-intercept of 2
   e) perpendicular to the line 3y+4x=18, and that passes through the origin
  
   please answer all these question

Sagot :

iloveonedirection
Lines that are parallel will have the same slope. Lines that are perpendicular will have slopes that are the negative reciprocal of each other.

(a) parallel to the line y=2x-4, and has a y-intercept of 7
slope of first line: 2
slope of second line: 2
y=mx + b
y=2x+7

(b) parallel to the line y-3x=6, and has a y-intercept of -2
y=3x+6
slope of first line: 3
slope of second line: 3
y=mx + b
y=3x-2

(c) parallel to the line 2x+3y=12, and that passes through the origin
3y=-2x+12
y=-2/3x+4
slope of first line: -2/3
slope of second line: -2/3
origin: (0,0)
y=mx + b
y=-2/3x + 0
y=-2/3x

(d) perpendicular to the line y=3x+2, and has a y-intercept of 2
slope of first line: 3
slope of second line: -1/3
y=mx + b
y=-1/3x + 2

(e) perpendicular to the line 3y+4x=18, and that passes through the origin
3y=4x+18
y=4/3x+6
slope of first line: 4/3
slope of second line: -3/4
origin: (0,0)
y=mx + b
y=-3/4x + 0
y=-3/4x
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