Question 532127: I really need to know how to put point-slope equations in standard form, Ax+By=C
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Consider the slope-intercept equation
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y = 5/2*x + 3/2
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multiply both sides by 2 to eliminate the fractions
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2(y) = 2(5/2x + 3/2)
2y = 2*5/2x + 2*3/2
2y = 5x + 3
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subtract 5x from both sides to get to standard form
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-5x + 2y = 3
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To define the point slope form of this equation requires two points.
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Recall: y = 5/2*x + 3/2
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m = slope = 5/2
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If x = 0, then y = 3/2, which is the y-intercept
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Find the x-intercept by setting y = 0 and solving for 'x'
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0 = 5/2*x + 3/2
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Multiply both sides by 2 to eliminate the fractions
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0 = 5x + 3
-5x = 3
x = -(3/5), which defines the point (-3/5,0)
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You now have two points: (0,3/2) and (-3/5,0)
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With two points you can set up the point-slope form.
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(y -y1) = m(x-x1)
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From above you know the slope is 5/2, so substitute the points and the slope.
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(3/2-0) = 5/2*(0-(-3/5))
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Checking this, we find.
3/2 = 5/2*(3/5)
3/2 = 15/10
True
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Done.
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