document.write( "Question 582247: How do I use an equation in point slope form (y + 5 = -1/2(x - 4)
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Algebra.Com's Answer #372029 by KMST(5328) $\"\"$ $\"About$

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The point slope form of a linear equation is the first form you write, when you only know the slope and the coordinates of a point. After that you may transform it into an equivalent equation in another form, depending on what you need to do with it.
\n" ); document.write( "How you use $\"y+%2B+5+=+%28-1%2F2%29%28x+-+4%29\"$ depends on what you want to use it for.
\n" ); document.write( "The equation represents a line with slope $\"-1%2F2\"$ that passes through point (4,-5).
\n" ); document.write( "You know that much from the equation.
\n" ); document.write( "The numbers subtracted from x and y are the coordinates of the point in the point slope form of the equation.
\n" ); document.write( "The slope is the number multiplying the x. (The slope is used to find out if the line is parallel or perpendicular to another line).
\n" ); document.write( "The point and the slope from the equation can be a good start to graph the line.
\n" ); document.write( "There are infinite equations in point slope form for the same line. Each point in the line can be used to get a different (but equivalent) equation.
\n" ); document.write( "If a problem asks to write the equation of the line passing through point (-8,1) with slope -1/2, you would first write
\n" ); document.write( " $\"y-1=%28-1%2F2%29%28x-%28-8%29%29\"$ --> $\"y-1=%28-1%2F2%29%28x%2B8%29\"$
\n" ); document.write( "Then you could transform it:
\n" ); document.write( " $\"y-1=%28-1%2F2%29%28x%2B8%29\"$ --> $\"y-1=%28-1%2F2%29x-4\"$ --> $\"y=%28-1%2F2%29x-3\"$
\n" ); document.write( "Similarly, for $\"y+%2B+5+=%28-1%2F2%29%28x+-+4%29\"$ :
\n" ); document.write( " $\"y+%2B+5+=+%28-1%2F2%29%28x+-+4%29\"$ --> $\"y%2B5=%28-1%2F2%29x%2B2\"$ --> $\"y=%28-1%2F2%29x-3\"$
\n" ); document.write( " $\"y=%28-1%2F2%29x-3\"$ is in slope intercept form.
\n" ); document.write( "You can see from the equation that the y-intercept is $\"-3\"$ . The line crosses the y axis (the line x=0) at (point (0,-3).
\n" ); document.write( "The beauty of the slope intercept form is that there is only one for each line. Besides, it gives you the direct recipe to calculate y for any x.
\n" ); document.write( " $\"y=%28-1%2F2%29x-3\"$ can also be transformed into $\"2y=-x-6\"$ by multiplying both sides times 2.
\n" ); document.write( "You can then add x to both sides to get $\"x%2B2y=-6\"$ .
\n" ); document.write( "You can transform it into many other equivalent equations, like
\n" ); document.write( " $\"x%2B2y%2B6=0\"$ or $\"5x%2B10y=-30\"$ . \n" ); document.write( "

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