Find the value of $y$ , if the line joining $(3, y)$ and $(2, 7)$ is parallel to the line joining the points $(- 1, 4)$ and $(0, 6)$ .

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Solution

In case of parallel slope is equal
$\begin{matrix} m_{1} = m_{2} & (\begin{matrix} X_{1}, Y_{1} 3, y \end{matrix}) a n d (\begin{matrix} X_{2}, Y_{2} 2, 7 \end{matrix}) \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} & (\begin{matrix} X_{1} Y_{1} - 1, 4 \end{matrix}) a n d (\begin{matrix} X_{2}, Y_{2} 0, 6 \end{matrix}) \frac{7 - y}{2 - 3} = \frac{6 - 4}{0 + 1} 7 - y = - 1 \times 2 7 + 2 = y y = 9 \end{matrix}$

Hence, this is the answer.

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