What is the equation of the line that passes through $(- 1, 3)$ $(-1,3)$ and is perpendicular to the line that passes through the following points: $(6, - 4), (5, 2)$ $(6,-4),(5,2)$ ?

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What is the equation of the line that passes through $(- 1, 3)$ $(-1,3)$ and is perpendicular to the line that passes through the following points: $(6, - 4), (5, 2)$ $(6,-4),(5,2)$ ?

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Answer 1 · 2016-01-06T16:51:52

Final answer: $6 y = x + 19$ $6y=x+19$ oe.

Explanation:

Defining line that passes through $a : (- 1, 3)$ $a:(-1, 3)$ as $l_{1}$ $l_1$ .
Defining line that passes through $b : (6, - 4), c : (5, 2)$ $b:(6, -4), c:(5, 2)$ as $l_{2}$ $l_2$ .

Find the gradient of $l_{2}$ $l_2$ .
$m_{2} = \frac{y_{b} - y_{c}}{x_{b} - x_{c}} = \frac{- 4 - 2}{6 - 5} = - 6$ $m_2=(y_b-y_c)/(x_b-x_c)=(-4-2)/(6-5)=-6$

$l_{2} ⊥ l_{1}$ $l_2_|_l_1$

So $m_{1} = - \frac{1}{m_{2}} = - \frac{1}{- 6} = \frac{1}{6}$ $m_1=-1/m_2=-1/-6=1/6$

Equation of $l_{1}$ $l_1$ :
$y - y_{a} = m_{1} (x - x_{a})$ $y-y_a=m_1(x-x_a)$

$y - 3 = \frac{1}{6} (x + 1)$ $y-3=1/6(x+1)$

$6 y - 18 = x + 1$ $6y-18=x+1$

$6 y = x + 19$ $6y=x+19$

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What is the equation of the line that passes through $(- 1, 3)$ $(-1,3)$ and is perpendicular to the line that passes through the following points: $(6, - 4), (5, 2)$ $(6,-4),(5,2)$ ?

1 Answer

Explanation:

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What is the equation of the line that passes through (−1,3)(-1,3) and is perpendicular to the line that passes through the following points: (6,−4),(5,2)(6,-4),(5,2)?

1 Answer

Explanation:

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What is the equation of the line that passes through $(- 1, 3)$ $(-1,3)$ and is perpendicular to the line that passes through the following points: $(6, - 4), (5, 2)$ $(6,-4),(5,2)$ ?