Date: Thu, 22 Apr 1999 20:22:21 -0600

My name is Crystal and I am in 9th grade algebra. We are currently studying parallel and perpendicular lines. I am having trouble with this problem: 3/4x - 5y= 16, (5,-6) I have to find a line that is perpindicular to this line on a graph.
Sincerely, Crystal

Hi Crystal

The crutial fact you need to use about perpendicular lines is that if a line had slope m then any line perpendicular to it has slope -1/m. The first job here is to find the slope of the line 3/4x - 5y = 16.
   If you write the equation of a line in the form y = mx + b then m is the slope. To write 3/4x - 5y = 16 in this form first subtract 3/4x from both sides to get -5y = 16 - 3/4x. If you now divide both sides by -5 the resulting equation is y = 3/20x + 16/5. Thus the slope of the line 3/4x - 5y = 16 is 3/20 and hence the slope of any perpendicular line is -1/(3/20) = -20/3. All that remains is to write the equation of the line through (5,-6) with slope -20/3.


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