Question

What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−2/3x+5 ?

Answer 1

Let $k:y=m_1x+b_1$ and $l:y=m_2x+b_2$

$l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have $y=-\dfrac{2}{3}x+5\to _1=-\dfrac{2}{3}$

Therefore

$m_2=-\dfrac{1}{-\frac{2}{3}}=\dfrac{3}{2}$

We have the equation of a line: $y=\dfrac{3}{2}x+b$.

Put the coordinates of the point (8, 1) to the equation of a line:

$1=\dfrac{3}{2}(8)+b$

$1=(3)(4)+b$

$1=12+b$       subtract 11 from both sides

$-11=b\to b=-11$

Answer: $\boxed{y=\dfrac{3}{2}x-11}$