Question 53851
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My problem is (3/4, 8/3) and (2/5, 2/3).
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I am supposed to find the slope and put the problem into slope intercept form and then into standard form (Ax+By=C).
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the slope equation: m = {{{(y2 - y1)/(x2 - x1)}}}
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In this problem x1 = 3/4; y1 = 8/3, x2 = 2/5, y2 = 2/3
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Let's get rid of these annoying fractions, mult them all by 60, it won't affect the value of the slope
Then we have x1 = 45, y1 = 160, x2 = 24, y2 = 40

m = {{{((40)-(160))/((24)-(45))}}}={{{(-120)/(-21)}}}={{{40/7}}}
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m = (40/7)  x1 = 3/4, y1 = 8/3
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Substitute in point/slope equation: y - y1 = m(x-x1)
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y - 8/3 = (40/7)m(x - 3/4)
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y - 8/3 = (40/7)x - (40/7)(3/4)
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y - 8/3 = (40/7)x - 120/28
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y - 8/3  = (40/7)x - 30/7  reduced the fraction
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y = (40/7)x - 30/7 + 8/3
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y = (40/7)x - 90/21 + 56/21
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y = (40/7)x - 34/21; this is the slope/intercept equation (y = mx+b)
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-21y = -120x + 34;  multiplied eq by -21
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120x - 21y = 34 is the standard form