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=-(1)/(m_1)`

We have

`y=-(1)/(3)x+4\to m_1=-(1)/(3)`

Therefore

`m_2=-(1)/(-(1)/(3))=(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