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Question
What is the value of y so that the line through (3, y) and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?
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Solution
Let m1 be the slope of the line passing through (3, y) and (2, 7) and m2 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.
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