Question

The line passing through (0, 2) and (−3, −1) is parallel to the line passing through (−1, 5) and (4, a) find a.​

Answer 1

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Answer 2

Given :-

• The line passing through (0, 2) and (−3, −1) is parallel to the line passing through (−1, 5) and (4, a)

To Find :-

• Value of a

Solution :-

• We know that

$\bf Slope = \dfrac{y_2 - y_1}{x_2-x_1}$

$\sf Slope = \dfrac{-1 - 2}{-3 - 0}$

$\sf Slope = \dfrac{-3}{-3}$

$\sf Slope = \dfrac{3}{3}$

$\sf Slope = 1$

Also,

$\bf Slope = \dfrac{y_2 - y_1}{x_2-x_1}$

$\sf Slope = \dfrac{a-5}{4-(-1)}$

$\sf Slope = \dfrac{a-5}{4+1}$

$\sf Slope = \dfrac{a-5}{5}$

Since, they are in parallel. Their slope must be equal

$\sf Slope_{1}=Slope_{2}$

$\sf 1 = \dfrac{a-5}{5}$

$\sf 1\times 5$

$\sf 5 = a-55$

$\sf -a = -5 - 5−a$

$\sf -a=-10−a$

$\sf a=10a$