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What is the value of y so that the line ...

What is the value of `y` so that the line through `(3,y)a n d(2,7)` is parallel to the line through `(-1,4)a n d(0,6)?`

Text Solution

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Let `A(3,y),B(2,7),C(-1,4)and D(0,6)` be the given points.
Then `m_(1)=` slope of the line `AB=(7-y)/(2-3)=y-7`
`m_(2)=` slope of line `CD=(6-4)/(0-(-1))=2`
Since AB and CD are parallel.
`m_(1)=m_(2)`
`impliesy-7=2`
`impliesy=9`
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