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)?`

Explanation

Let `{m}_{1}` be the slope of the line passing through `(3, y)` and `(2,7)` and `{m}_{2}` be the slope of the line passing through `(-1,4)` and `(0,6)`.

`therefore m_{1}=frac{y_{2}-y_{1}}{x_{2}-x_{1}}=frac{7-y}{2-3}=frac{7-y}{-1}=y-7` and `m_{2}=frac{y_{2}-y_{1}}{x_{2}-x_{1}}=frac{6-4}{0+1}=frac{2}{1}=2`

For both the lines to be parallel, we must have,

`m_{1}=m_{2}`

`Rightarrow y-7=2`

`Rightarrow y=9`

Hence, the value of `y` is 9 .