SOLUTION: What is the equation of the line described below written in slope-intercept form? the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0

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Question 822202: What is the equation of the line described below written in slope-intercept form?
the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0

y = -x
y = -x
y = x
Found 2 solutions by rothauserc, MathLover1:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
first put this equation 3x + 2y - 6 = 0 in standard y = mx +b format
2y = -3x +6
divide both sides of = by 2
y = -3x/2 +3
use slope -3/2 and point (0, 0) note that parallel lines have same slope
(y -0 ) = -3/2 * (x - 0)
y = -3x/2


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
the equation of the line described below written in slope-intercept form the line passing through point ( ++0++, ++0++ ) and parallel to the line whose equation is 3x+%2B+2y+-+6+=+0
first write 3x+%2B+2y+-+6+=+0 in slope-intercept form

+2y++=+-3x%2B6
+y++=+-%283%2F2%29x%2B6%2F2
+y++=+-%283%2F2%29x%2B3
now, find the equation of the line passing through point ( ++0++, ++0++ ) and parallel to the line whose equation is +y++=+-%283%2F2%29x%2B3

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is -1.5 (its from the slope of y=-1.5%2Ax%2B3 which is also -1.5). Also since the unknown line goes through (0,0), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y-0=-1.5%2A%28x-0%29 Plug in m=-1.5, x%5B1%5D=0, and y%5B1%5D=0



y-0=-1.5%2Ax%2B%281.5%29%280%29 Distribute -1.5



y-0=-1.5%2Ax-0 Multiply



y=-1.5%2Ax-0%2B0Add 0 to both sides to isolate y

y=-1.5%2Ax%2B0 Combine like terms

So the equation of the line that is parallel to y=-1.5%2Ax%2B3 and goes through (0,0) is y=-1.5%2Ax%2B0


So here are the graphs of the equations y=-1.5%2Ax%2B3 and y=-1.5%2Ax%2B0



graph of the given equation y=-1.5%2Ax%2B3 (red) and graph of the line y=-1.5%2Ax%2B0(green) that is parallel to the given graph and goes through (0,0)