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General form of the line

Updated: 4/28/2022
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Ax+By+C=0

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Q: General form of the line
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Why did the Confederacy won the Battle of Chickamauga?

The crucial events happened on the second day of the battle, September 20, 1863. The Union commander was Major General William S. Rosecrans. He received a report at his headquarters from an officer who had just ridden to his headquarters up the road immediately behind the Union line. This officer had failed to see a brigade in the Union line which was concealed in the underbrush and trees, and reported to Rosecrans that there was a huge gap in the line, meaning the line was not connected. Without further investigation Rosecrans immediately sent orders to Brigadier General Thomas J. Wood, who was commanding a brigade which was in line just to the south of where the alleged gap in the Union line was located. The orders were peremptory and abrupt in tone, and ordered Wood to move his brigade to the left, to link his left with the right of the brigade just to the north of the alleged gap. Though this made no sense, because Wood was aware of the brigade which was already to his left which the officer had not seen who reported to Rosecrans, the last time Wood had spoken to Rosecrans the commander had insulted and humiliated him by upbraiding him in front of his staff for not following orders fast enough to suit Rosecrans. So even though there was another brigade in the way of where Wood was ordered to go, he pulled his men out of the line to begin moving north, to his left. Thus, where no gap had existed, Rosecrans orders to Wood and Wood's prompt obedience to those orders did create a brigade-wide gap in the Union line. During the previous night Lieutenant General James Longstreet had arrived on the field with two divisions from General Lee' army. He was given a third division by the Rebel commander at Chickamauga, General Braxton Bragg. Longstreet had just finished arranging the eight brigades of these three divisions into a powerful attacking column, five lines deep. He sent these forward and, with the worst of all possible luck for the Yankees, Longstreet's attack hit the gap just created when Wood pulled out of line in obedience to Rosecrans orders. This massive breakthrough caused the Yankees to panic and their entire line collapsed, as the Rebels spread behind both flanks of their breakthrough and started shooting Yankees from behind.

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The slope intercept form of the equation of a line is: y = mx + b The general form is: Ax + By + C = 0 So, when the line is given in the slope intercept form, the general form will be mx - y + b = 0


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y=mx + b


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The general form is 11x - 10y + 19 = 0


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The general equation is y = mx + c. m is the slope of the straight line. c is the y intercept. This is readily obtained by putting x = 0 then the general equation simplifies to y = c.


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y = 6/7x+3 General form of the line equation: 6x -7y+21 = 0


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