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put this solution on YOUR website!Hi, Hope I can help,
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Write an equation of the Line 1 passing through (3,-4) that is parallel to the Line II 5x-3y-9=0. Does the line I pass through the point (6,7)? Does the line II pass through the point (6,7)?
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First, we have to put Line II in slope-intercept form (y = Ax+b)("A" is the slope)
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5x-3y-9=0
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We will move (-3y) to the right side
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5x - 3y + 3y - 9 = 0 + 3y
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5x - 9 = 3y
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3y = 5x - 9
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We will now divide each side by "3"
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y =
x - 3
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(y =
x - 3) is the slope-intercept form of Line II
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Since Line I is parallel to Line II, it has the same slope
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Equation to Line I
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y =
x + b
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We can solve "b" by replacing "x" and "y" with (3,-4)(x,y)(Since the line contains that point
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We will multiply the right side
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We will move "5" to the left side
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b = (-9), we can replace "b" in our equation
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y =
x + b
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y =
x + (-9)
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y =
x - 9
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(y =
x - 9) is the slope-intercept equation to Line I
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You can check by replacing "x" and "y" with (3, -4)(x,y)
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(y =
x - 9) is the correct equation to Line I
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y =
x - 9( to get a different form of equation, you get rid of the fraction)(We will multiply each side by "3")
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3y = 5x - 27
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We will move "3y" to the right side
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3y - 3y = 5x - 3y - 27
0 = 5x - 3y - 27
(5x - 3y - 27 = 0) is another form,( you can move (-27) over, and it will become
( this is the standard form)
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To see if (6,7) is a point of either of the two lines, you will replace "x" and "y" with (6,7)(x,y)
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First equation,
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This is not true, so point (6,7) is not a point on the first line.
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Second line
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5x-3y-9=0 ( standard form = (5x - 3y = 9)(moved (-9) to the right side)
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5x - 3y = 9
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We can replace "x" and "y" with (6,7)(x,y)
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5(6) - 3(7) = 9
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30 - 21 = 9
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(9 = 9) This is true, (6,7) is a point on Line II
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Hope I helped, Levi
