SOLUTION: Write the equation of a line that passes through the point (7,1) and is perpendicular to the line with the equation 6x-3y=8. I've tried solving this and had some trouble.

Algebra ->  Formulas -> SOLUTION: Write the equation of a line that passes through the point (7,1) and is perpendicular to the line with the equation 6x-3y=8. I've tried solving this and had some trouble.       Log On


   

Question 1053974: Write the equation of a line that passes through the point (7,1) and is perpendicular to the line with the equation 6x-3y=8. I've tried solving this and had some trouble.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First put the given equation into
the slope-intercept form
+6x+-+3y+=+8+
+-3y+=+-6x+%2B+8+
+3y+=+6x+-+8+
+y+=+2x+-+8%2F3+
---------------------
Any line perpendicular to this line
will have slope = +m%5B2%5D+=+-1%2Fm%5B1%5D+
where +m%5B1%5D+=+2+
------------------------------------
+m%5B2%5D+=+-1%2F2+
given the point ( 7, 1 )
Now use the general point-slope formula
+%28+y+-+1+%29+%2F+%28+x+-+7+%29+=+-1%2F2+
+y+-+1+=+%28-1%2F2%29%2A%28+x+-+7+%29+
+y+=+%28-1%2F2%29%2A%28+x+-+7+%29+%2B+2%2F2+
+y+=+%28-1%2F2%29%2Ax+%2B+7%2F2+%2B+2%2F2+
+y+=+%28-1%2F2%29%2Ax+%2B+9%2F2+
--------------------------------
check:
Does it go through ( 7,1 ) ?
+1+=+%28-1%2F2%29%2A7+%2B+9%2F2+
+1+=+-7%2F2+%2B+9%2F2+
+2%2F2+=+2%2F2+
OK
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Here's a plot of both lines: