document.write( "Question 211337: Please me find the equation of the line going through the point (-2,-3) and perpendicular to -2X+3Y=8 \n" ); document.write( "

Algebra.Com's Answer #159697 by Earlsdon(6294) $\"\"$ $\"About$

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First find the slope of the given line:
\n" ); document.write( " $\"-2x%2B3y+=+8\"$ Add 2x to both sides.
\n" ); document.write( " $\"3y+=+2x%2B8\"$ Divide both sides by 2.
\n" ); document.write( " $\"y+=+%282%2F3%29x%2B8%2F3\"$ Compare this with the slope-intercept form:
\n" ); document.write( " $\"y+=+mx%2Bb\"$
\n" ); document.write( "The slope is: $\"m+=+2%2F3\"$ If a line is perpendicular to this, its slope will be the negative reciprocal or $\"m+=+-3%2F2\"$ so we can start with:
\n" ); document.write( " $\"y+=+%28-3%2F2%29x%2Bb\"$ Now we find b by substituting the x- and y-coordinates from the given point:
\n" ); document.write( " $\"-3+=+%28-3%2F2%29%28-2%29%2Bb\"$
\n" ); document.write( " $\"-3+=+3%2Bb\"$
\n" ); document.write( " $\"b+=+-6\"$
\n" ); document.write( "The equation is:
\n" ); document.write( " $\"y+=+%28-3%2F2%29x-6\"$ \n" ); document.write( "

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