document.write( "Question 825581: Explain in words how to write an equation that is part one: parallel and then also part two: perpendicular to the equation y=2/3x-4 passing through the point (-2,-5). \n" ); document.write( "

Algebra.Com's Answer #497421 by math-vortex(648) $\"\"$ $\"About$

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document.write( "Hi there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Explain in words how to write an equation that is part one: parallel and then also part two: \r\n" );
document.write( "perpendicular to the equation y=2/3x-4 passing through the point (-2,-5).\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Part I:\r\n" );
document.write( "To write the equation of a line that is parallel to another line, we use the mathematical idea \r\n" );
document.write( "that parallel lines have the same slope. \r\n" );
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document.write( "Your line  is in slope intercept form (y=mx+b). In this form, the slope of the \r\n" );
document.write( "line is the coefficient of the x-term. In other words, the slope is 2/3.\r\n" );
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document.write( "Now we know the slope of the parallel line as well as a point (-2,-5) that the line passes \r\n" );
document.write( "through. We can build an equation using the point-slope form for the equation of a line.\r\n" );
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document.write( "In this formula, m is the slope of the line,  and  are the x- and \r\n" );
document.write( "y-coordinates of a point on the line. Substituting, we have the equation\r\n" );
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document.write( "This is an equation for the line parallel to the line  through (-2,-5).\r\n" );
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document.write( "If you want, you can simplify the equation by clearing the parentheses and combining like \r\n" );
document.write( "terms.\r\n" );
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document.write( "Part II:\r\n" );
document.write( "To write an equation for a perpendicular line, we use the mathematical idea that when two \r\n" );
document.write( "lines are perpendicular, the product of their slopes is -1. (The official mathematical language \r\n" );
document.write( "for this is \"one slope is the negative reciprocal of the other slope.\")\r\n" );
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document.write( "For example, if the slope of one line is 3/4, the slope of the other is -4/3 because\r\n" );
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document.write( "After you find the slope of the perpendicular line, you use the point-slope formula as we did \r\n" );
document.write( "above to find the equation of the line.\r\n" );
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document.write( "Hope that helps! Feel free to email me if you have questions about this explanation.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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