Question

Write an equation of a line that passes through (4,3) and is perpendicular to the graph of the equation y=-1/3x + 4.

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

$y=-\dfrac{1}{3}x+4\to m_1=-\dfrac{1}{3}$

Therefore

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

We have the equation of a line:

$y=3x+b$

Put the coordinates of the point (4, 3) to the equation of a line:

$3=3(4)+b$

$3=12+b$         subtract 12 from both sides

$-9=b\to b=-9$

Answer: y = 3x - 9