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

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Answer 1 · 2016-01-06T16:51:52

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

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

Find the gradient of $l_2$ .
$m_2=(y_b-y_c)/(x_b-x_c)=(-4-2)/(6-5)=-6$

$l_2_|_l_1$

So $m_1=-1/m_2=-1/-6=1/6$

Equation of $l_1$ :
$y-y_a=m_1(x-x_a)$

$y-3=1/6(x+1)$

$6y-18=x+1$

$6y=x+19$

Or however you want it arranged.

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)?