SOLUTION: what is the equation form passing through lines (1,3)and (-1,2)
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Question 3630: what is the equation form passing through lines (1,3)and (-1,2)
Answer by AnlytcPhil(1810) (Show Source): You can put this solution on YOUR website!
>>...What is the equation form passing through lines (1,3) and (-1,2)...<<
`
The equation of the line passing through two points (x1,y1) and (x2,y2)
is:
`
` ` `y - y1 = m(x - x1)
`
where
``
` ` ` ` ` y2 - y1
` ` `m = —————————
` ` ` ` ` x2 - x1
`
In this case (x1,y1) = (1,3) and (x2,y2) = (-1,2)
`
First substitute in the formula for m:
`
` ` ` ` ` y2 - y1
` ` `m = —————————
` ` ` ` ` x2 - x1
`
` ` ` ` ` (2) - (3)
` ` `m = ———————————
` ` ` ` `(-1) - (1)
`
` ` ` ` `-1` ` `1
` ` `m = ——— = ———
` ` ` ` `-2` ` `2
`
Now substitute 1/2 for m, 1 for x1, 3 for y1, -1 for x2 and 3 for y2
in the formula
`
` ` `y - y1 = m(x - x1)
`
` ` ` y - 3 = (1/2)(x - 1)
`
Now clear of fractions by multiplying both side by 2
`
` `2[y - 3] = 2[(1/2)(x - 1]
`
` `2[y - 3] = 2[1/2)(x - 1]
`
` ` `2y - 6 = x - 1
`
The standard form is to have the x-term first, then the y-term,
then an equal sign and then a number:
`
` ` `-x + 2y = 6 - 1
`
` ` `-x + 2y = 5
`
The standard form is considered best when the x-term is positive,
so multiply through by -1
`
` ` ` `x - 2y = -5
`
Edwin J
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