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WAEC Mathematics 2023 Paper

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Question : 27

Total: 50

A line L passing through the point (6, -13) is parallel to the line which passes through (7, 4) and (-3, 9). Find the equation of the line L.

y = $\frac{1}{2}x - 10$
y = $\frac{-1}{2}x + 10$
y = $\frac{-1}{2}x - 10$
y = $\frac{1}{2}x + 10$

Solution:

(7, 4) and (-3, 9) = ( $y_1 , x_1)(y_2 , x_2)$

slope $m_1$ of the points(7, 4) and (-3, 9) = $\frac{y_2 - y_1}{x_2 - x_1}$

$m_1 = \frac{9-4}{-3-7} = \frac{5}{-10} = \frac{-1}{2}$

$m_1 = m_2$ ( condition for parallelism)

Since the line L passes through the point (6, -13) and is parallel to the points (7, 4) and (-3, 9)

$\frac{-1}{2} = \frac{y - (-13)}{x - 6}$

= $\frac{-1}{2} = \frac{y + 13}{x - 6}$

= $\frac{-1}{2}(x - 6) = y + 13$

$\frac{-1}{2}x + 3 = y + 13$

= $\frac{-1}{2}x + 3 - 13 = y$

∴ y = $\frac{-1}{2}x - 10$

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