document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200271>Question 1200271</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the line through the points (-5,3) and (-6,-1). Express the equation of the line in slope=intercept form, y=mx+b.\r<BR>\n" );
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document.write( "So I know y2-y1/x2-x1 so I did that (-1-3/-6-(-5)=(-4/1)\r<BR>\n" );
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document.write( "y=mx+b so 3=-(4/1)(-5)+b<BR>\n" );
document.write( "solved for that to get b=-17 <BR>\n" );
document.write( "y=(-4/1)x-17\r<BR>\n" );
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document.write( "Your basic process is fine.  But you got off on the wrong foot by calculating the slope incorrectly.<br><BR>\n" );
document.write( "You calculated the slope as -4 and then used the point (-5,3) to find your equation y=-4x-17.  That part of your process was fine; but the slope you found was not right.  If you had also checked the point (-6,-1) with your slope of -4, you would have seen that something was wrong.<br><BR>\n" );
document.write( "I have seen probably hundreds of cases where a student calculated the slope of a line through two given points incorrectly by plugging the wrong numbers in the slope formula, or by making arithmetic errors in the calculation (as you did: -6-(-5) is -1, not 1).<br><BR>\n" );
document.write( "I would recommend NOT using the slope formula but rather drawing a quick sketch -- on paper, or at least in your mind -- of the two given points.  In your example, even a very rough sketch would show that the line goes up as you move to the right, which means the slope is positive, so the slope of -4 you calculated could not be right.<br><BR>\n" );
document.write( "So IF you use the slope formula to calculate the slope, then at least use a sketch to see if the slope you calculate is reasonable.<br><BR>\n" );
document.write( "But using the sketch to find the rise and run -- and thus to determine the slope -- is much easier with a sketch than with a formula.  A quick sketch of the two given points shows the run (from -6 to -5) is 1 and the rise (from -1 to 3) is 4, so the slope is -4/-1 = 4, not -4/1 = -4.<br><BR>\n" );
document.write( "Then, with the correct slope of 4 instead of -4 and EITHER of the two points, you can come up with the correct equation y = 4x+23.<br><BR>\n" );
document.write( "So here again is my recommendation:<br><BR>\n" );
document.write( "On a few examples, try calculating slopes by drawing a rough sketch and using the rise and run that you get from the sketch.  But if that doesn't \"work\" for you, then use the slope formula -- but make a quick sketch to see if the slope you calculate using the formula is reasonable.<br><BR>\n" );
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