document.write( "Question 37207: Write the equation of the line L satisfying the given geometric conditions.
\n" ); document.write( "L has y-intercept (0,2) and is perpendicular to the line with equation 2x-3y=6\r
\n" ); document.write( "\n" ); document.write( "I am able to solve this style of equation when the line is parallel and when the y variable is already by itself. I can't seem to figure this one out. Help, please!
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Algebra.Com's Answer #22943 by Nate(3500)\"\" \"About 
You can put this solution on YOUR website!
First, let us determine the slope of the equation:
\n" ); document.write( "2x-3y=6
\n" ); document.write( "-3y=-2x+6
\n" ); document.write( "y=(2/3)x-2
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Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation \"2+x+%2B+-3+y+=+6\" describes a sloping line. For any
\n" ); document.write( " equation ax+by+c = 0, slope is \"-a%2Fb+=+-2%2F-3\".
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 6/2 = 3.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 6/-3 = -2.
  • Slope is -2/-3 = 0.666666666666667.
  • Equation in slope-intercept form: y=0.666666666666667*x+-2.
\"graph%28+500%2C+500%2C+3-8%2C+3%2B8%2C+-2-8%2C+-2%2B8%2C+0.666666666666667%2Ax%2B-2+%29+\"\n" ); document.write( "

\n" ); document.write( "\n" ); document.write( "The slope is perpendicular to (2/3), so the slope is the opposite of the recipricol (-3/2).
\n" ); document.write( "Write the equation of the line L satisfying the given geometric conditions.
\n" ); document.write( "L has y-intercept (0,2).
\n" ); document.write( "use: y-(y point)=m(x-(x point))
\n" ); document.write( "y-2=(-3/2)x
\n" ); document.write( "y=(-3/2)x+2 the equation
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Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc
Equation \"1.5+x+%2B+1+y+=+2\" describes a sloping line. For any
\n" ); document.write( " equation ax+by+c = 0, slope is \"-a%2Fb+=+-1.5%2F1\".
  • X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 2/1.5 = 1.33333333333333.
  • Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 2/1 = 2.
  • Slope is -1.5/1 = -1.5.
  • Equation in slope-intercept form: y=-1.5*x+2.
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