document.write( "Question 159100: Determine the value of \"a\" so that the line through (5,8) and (a,6) has a slope of -3/4 \n" ); document.write( "
Algebra.Com's Answer #117227 by Electrified_Levi(103)\"\" \"About 
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Hi, Hope I can help,
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\n" ); document.write( "Determine the value of \"a\" so that the line through (5,8) and (a,6) has a slope of \"+-3%2F4+\"
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\n" ); document.write( "First we have to know what the slope is. The slope is how steep the line is. It is the slant of the line
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\n" ); document.write( "These lines have negative slopes
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\n" ); document.write( "\"+graph+%28600%2C600%2C-10%2C10%2C-10%2C10%2C-x%2C-3x%2B2%2C-2x-4+%29+\"
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\n" ); document.write( "As you can see, a slope that is negative means, the line (from left to right) is going down
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\n" ); document.write( "Here are some lines with positive slopes
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\n" ); document.write( "\"+graph+%28600%2C600%2C-10%2C10%2C-10%2C10%2C2x%2Cx-6%2C5x%2B1+%29+\"
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\n" ); document.write( "As you can see a slope that is positive, means the line(from left to right) is going up
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\n" ); document.write( "Now that you know a little about slopes lets do the problem
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\n" ); document.write( "Determine the value of \"a\" so that the line through (5,8) and (a,6) has a slope of \"+-3%2F4+\"
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\n" ); document.write( "The slope is negative, so the line is going down(from left to right)
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\n" ); document.write( "Here is one way to solve this kind of problem
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\n" ); document.write( "If the point is (2,4) find a point (6,c) if the slope is \"+-7%2F4+\"
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\n" ); document.write( "The slope is negative, so the line is going down.
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\n" ); document.write( "The slope is \"+rise%2Frun+\", or \"+%28up-or-down%29%2F%28left-or-right%29+\"
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\n" ); document.write( "Since the slope is negative, \"+-7%2F4+\",
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\n" ); document.write( "A slope of \"+-7%2F4+\" means you go down \"7\" and over to the right \"4\" times
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\n" ); document.write( "If we do that, we will get our point
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\n" ); document.write( "The point is (6,-3)
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\n" ); document.write( "There is yet another way to solve this kind of problem
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\n" ); document.write( "Determine the value of \"a\" so that the line through (5,8) and (a,6) has a slope of \"+-3%2F4+\"
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\n" ); document.write( "We use the slope equation = \"+%28y2-y1%29%2F%28x2-x1%29+\"
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\n" ); document.write( "(ex. slope of (1,2)(x1,y1) and (2,4)(x2,y2), equation = \"+%28y2-y1%29%2F%28x2-x1%29+\"
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\n" ); document.write( "Replace the variables
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\n" ); document.write( "\"+%28y2-y1%29%2F%28x2-x1%29+\" = \"+%284-2%29%2F%282-1%29+\" = \"+2%2F1+\", these two lines have slope of \"2\"
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\n" ); document.write( "we can do the same for our problem
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\n" ); document.write( "Determine the value of \"a\" so that the line through (5,8)(x1,y1) and (a,6)(x2,y2) has a slope of \"+-3%2F4+\"
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\n" ); document.write( "Replace the variables in the equation = \"+%28y2-y1%29%2F%28x2-x1%29+\" = \"+%286-8%29%2F%28a-5%29+\" = \"+%28-2%29%2F%28a-5%29+\", we already know the slope, this equation we have = \"+-3%2F4+\"
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\n" ); document.write( "Our equation = \"+%28-2%29%2F%28a-5%29+=+-3%2F4+\", now just solve for \"a\"
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\n" ); document.write( "\"+%28-2%29%2F%28a-5%29+=+-3%2F4+\"
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\n" ); document.write( "We will use cross multiplication
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\n" ); document.write( "\"+highlight%28-2%29%2F%28a-5%29+=+-3%2Fhighlight%284%29+\" = \"+%28-2%29%2Fhighlight%28a-5%29+=+highlight%28-3%29%2F4+\" = \"+%28-8%29=+%28a-5%29%28-3%29+\" = \"+%28-8%29=+%28-3%29%28a-5%29+\"
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\n" ); document.write( "Using distribution
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\n" ); document.write( "\"+%28-8%29=+%28-3%29%28a-5%29+\" = \"+%28-8%29=+highlight%28-3%29%28highlight%28a%29-5%29+\" = \"+%28-8%29=+highlight%28-3%29%28a-highlight%285%29%29+\" = \"+%28-8%29=+%28-3a%29+%2B+15+\" ( since the \"5\" is negative, it will make a positive \"15\" since the \"3\" is negative too)
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\n" ); document.write( "We will move \"15\" to the left side
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\n" ); document.write( "\"+%28-8%29=+%28-3a%29+%2B+15+\" = \"+%28-8%29-15=+%28-3a%29+%2B+15-15+\" = \"+%28-23%29=+%28-3a%29+\"
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\n" ); document.write( "We will multiply each side by (-1)
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\n" ); document.write( "\"+%28-23%29=+%28-3a%29+\" = \"+%28-1%29%28-23%29=+%28-3a%29%28-1%29+\" = \"+23+=+3a+\" = \"+3a+=+23+\", divide each side by \"3\" to get our \"a\"
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\n" ); document.write( "\"+3a+=+23+\" = \"+3a%2F3+=+23%2F3+\" = \"+a+=+23%2F3+\"
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\n" ); document.write( "We can check by replacing \"a\" with \"+23%2F3+\" in our equation
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\n" ); document.write( "\"+%28-2%29%2F%28a-5%29+=+-3%2F4+\" = \"+%28-2%29%2F%28%2823%2F3%29-5%29+=+-3%2F4+\" = \"+%28-2%29%2F%28%2823%2F3%29-%2815%2F3%29%29+=+-3%2F4+\" = \"+%28-2%29%2F%288%2F3%29+=+-3%2F4+\" = \"+%28-2%2F1%29%283%2F8%29+=+-3%2F4+\" = \"+%28-6%2F8%29+=+-3%2F4+\" = \"+%28-3%2F4%29+=+%28-3%2F4%29+\" (True)
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\n" ); document.write( "a = \"+23%2F3+\"
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\n" ); document.write( "We found our point, if our point was (a,6), just replace \"a\" with \"+23%2F3+\", our point is (\"+23%2F3+\",6)
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\n" ); document.write( "Here are the two points
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\n" ); document.write( "Now draw a line through these points, this line has a slope of \"+-3%2F4+\"
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\n" ); document.write( "The line equation = \"+y+=+%28-3%2F4%29x+%2B+47%2F4+\" (slope -intercept form), or \"+3x+%2B+4y+=+47+\" (standard form)
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\n" ); document.write( "The point you were looking for is (\"+23%2F3+\",6)
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\n" ); document.write( "Your answer is (\"+23%2F3+\",6)
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\n" ); document.write( "Hope I helped, Levi
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