Question 159100: Determine the value of "a" so that the line through (5,8) and (a,6) has a slope of -3/4
Found 3 solutions by Fombitz, KnightOwlTutor, Electrified_Levi:
Answer by Fombitz(32388)   (Show Source):
Answer by KnightOwlTutor(293)  (Show Source):
You can put this solution on YOUR website! To determine the slope of the line M= y2-y1/x2-x1
(6-8)/(a-5)=-3/4
Cross multiply
4(-2)=-3a + 15
-8=-3a + 15
add 8 to both sides
0=-3a + 23
Add 3a to both sides
3a=23
divide both sides by 3
a=23/3
Plug in to check answer
I found the common denominator for the y values as 3
5X3=15
(6-8)/(23-15/3)=-2/8/3=-3/4
-2*inverse od 8/3 =-2*(3/8) simplfy the equation.
Answer by Electrified_Levi(103)  (Show Source):
You can put this solution on YOUR website! Hi, Hope I can help,
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Determine the value of "a" so that the line through (5,8) and (a,6) has a slope of 
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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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These lines have negative slopes
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As you can see, a slope that is negative means, the line (from left to right) is going down
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Here are some lines with positive slopes
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As you can see a slope that is positive, means the line(from left to right) is going up
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Now that you know a little about slopes lets do the problem
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Determine the value of "a" so that the line through (5,8) and (a,6) has a slope of
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The slope is negative, so the line is going down(from left to right)
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Here is one way to solve this kind of problem
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If the point is (2,4) find a point (6,c) if the slope is 
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The slope is negative, so the line is going down.
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The slope is  , or 
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Since the slope is negative, ,
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A slope of means you go down "7" and over to the right "4" times
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If we do that, we will get our point
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The point is (6,-3)
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There is yet another way to solve this kind of problem
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Determine the value of "a" so that the line through (5,8) and (a,6) has a slope of
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We use the slope equation = 
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(ex. slope of (1,2)(x1,y1) and (2,4)(x2,y2), equation =
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Replace the variables
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=  =  , these two lines have slope of "2"
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we can do the same for our problem
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Determine the value of "a" so that the line through (5,8)(x1,y1) and (a,6)(x2,y2) has a slope of
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Replace the variables in the equation = =  =  , we already know the slope, this equation we have =
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Our equation =  , now just solve for "a"
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We will use cross multiplication
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 =  =  = 
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Using distribution
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=  =  =  ( since the "5" is negative, it will make a positive "15" since the "3" is negative too)
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We will move "15" to the left side
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=  = 
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We will multiply each side by (-1)
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=  =  =  , divide each side by "3" to get our "a"
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=  = 
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We can check by replacing "a" with  in our equation
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=  =  =  =  =  =  (True)
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a =
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We found our point, if our point was (a,6), just replace "a" with , our point is (,6)
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Here are the two points
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Now draw a line through these points, this line has a slope of
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The line equation =  (slope -intercept form), or  (standard form)
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The point you were looking for is (,6)
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Your answer is (,6)
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Hope I helped, Levi
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