Question 3630
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>>...What is the equation form passing through lines (1,3) and (-1,2)...<<
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The equation of the line passing through two points (x<sub>1</sub>,y<sub>1</sub>) and (x<sub>2</sub>,y<sub>2</sub>) 
is: 
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` ` `y - y<sub>1</sub> = m(x - x<sub>1</sub>)
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where
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` ` ` ` ` y<sub>2</sub> - y<sub>1</sub>
` ` `m = —————————
` ` ` ` ` x<sub>2</sub> - x<sub>1</sub>
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In this case (x<sub>1</sub>,y<sub>1</sub>) = (1,3) and (x<sub>2</sub>,y<sub>2</sub>) = (-1,2)
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First substitute in the formula for m:
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` ` ` ` ` y<sub>2</sub> - y<sub>1</sub>
` ` `m = —————————
` ` ` ` ` x<sub>2</sub> - x<sub>1</sub>
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` ` ` ` ` (2) - (3)
` ` `m = ———————————
` ` ` ` `(-1) - (1)
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` ` ` ` `-1` ` `1
` ` `m = ——— = ———
` ` ` ` `-2` ` `2
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Now substitute 1/2 for m, 1 for x<sub>1</sub>, 3 for y<sub>1</sub>, -1 for x<sub>2</sub> and 3 for y<sub>2</sub>
in the formula
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` ` `y - y<sub>1</sub> = m(x - x<sub>1</sub>)
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` ` ` y - 3 = (1/2)(x - 1)
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Now clear of fractions by multiplying both side by 2
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` `2[y - 3] = 2[(1/2)(x - 1]
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` `2[y - 3] = <s>2</s>[1/<s>2</s>)(x - 1]
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` ` `2y - 6 = x - 1
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The standard form is to have the x-term first, then the y-term, 
then an equal sign and then a number:
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` ` `-x + 2y = 6 - 1
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` ` `-x + 2y = 5
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The standard form is considered  best when the x-term is positive,
so multiply through by -1
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` ` ` `x - 2y = -5
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Edwin <font face = "wingdings" size = 7 color = "red">J</font>