SOLUTION: The equation of the line perpendicular to y= 1/3x + 8 and through (7,-4) Is what? Will you please show steps!

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Question 1046522: The equation of the line perpendicular to y= 1/3x + 8 and through (7,-4)
Is what?
Will you please show steps!
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
y%2B4=-3%28x-7%29


Steps were not shown. Do you know why, and how to see through the concepts quickly? If you want the equation result to be in slope-intercept form, you simply need to do a couple simple algebra steps.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+y+=+%281%2F3%29%2Ax+%2B+8+
This is a linear ( straight line ) equation which
is in the slope-intercept form. In general, the
slope-intercept form looks like:
+y+=+m%2Ax+%2B+b+
where +m+ = slope of the line
--------------------------------
In this case, +m+=+1%2F3+
The slope of ANY line perpendicular to
this line will have a slope of:
+m%5B1%5D+=+-1%2Fm+
+m%5B1%5D+=+-1%2F%28%281%2F3%29%29+
+m%5B1%5D+=+-3+
-----------------------
So far, you know the perpendicular line looks like:
+y+=+-3x+%2B+b+
The perpendicular line goes through ( 7,-4 )
Use the point-slope formula to find +b+
----------------------------------------
+%28+y+-+%28-4%29+%29+%2F+%28+x+-+7+%29+=+-3+
+y+%2B+4+=+-3%2A%28+x+-+7+%29+
+y+%2B+4+=+-3x+%2B+21+
+y+=+-3x+%2B+17+
-----------------------------
check answer:
does it go through ( 7,-4 ) ?
+y+=+-3x+%2B+17+
+-4+=+-3%2A7+%2B+17+
+-4+=+-21+%2B+17+
+-4+=+-4+
OK
Here is the plot of both lines:
+graph%28+500%2C+500%2C+-20%2C+20%2C+-20%2C+20%2C+%281%2F3%29%2Ax+%2B+8%2C+-3x+%2B+17+%29+