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)? - Mathematics

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)?

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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.1 | Q 6 | Page 13