document.write( "Question 152346This question is from textbook
\n" ); document.write( ": How do you find the slope with only one point to work with? The first point is (3,4). The problem I am trying to solve is: Consider the semicircle of radius 5 centered at (0,0) as shown in the figure. Find an equation of the line tangent to the semicircle at the point (3,4). (hint: A line tangent to a circle is perpendicular to the radius at the point of tangency.) \n" ); document.write( "

Algebra.Com's Answer #111994 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
I don't see the figure you allude to but it's easy enough imagine what it looks like.
\n" ); document.write( "In your semicircle, consider the radius from the center to the point of tangency (3, 4). This radius has a slope of $\"m+=+4%2F3\"$ (rise = 4 over run = 3). Now any line that is perpendicular to this radius. eg, the tangent line at (3, 4), will have a slope that is the negative reciprocal of the slope of this radius. So the slope of the tangent line will be $\"m+=+-3%2F4\"$
\n" ); document.write( "So now you can write:
\n" ); document.write( " $\"y+=+%28-3%2F4%29x%2Bb\"$ But of course, you still need to find the value of b, the y-intercept, so substitute the x- and y-coordinate values of the point of tangency (3, 4) into this equation and solve for b.
\n" ); document.write( " $\"y+=+%28-3%2F4%29x%2Bb\"$ Substitute x = 3 and y = 4
\n" ); document.write( " $\"4+=+%28-3%2F4%29%283%29%2Bb\"$ Solve for b.
\n" ); document.write( " $\"4+=+-9%2F4+%2B+b\"$
\n" ); document.write( " $\"b+=+25%2F4\"$
\n" ); document.write( "So your final equation would be:
\n" ); document.write( " $\"y+=+%28-3%2F4%29x%2B25%2F4\"$ or, if you multiply through by 4 to clear the fractions, it becomes:
\n" ); document.write( " $\"4y+=+-3x%2B25\"$ \n" ); document.write( "

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