Question

What is the equation of the line through (6, 9) and parallel to the line whose inclination is arctan 2​

Answer 1

Answer:

Step-by-step explanation:

The slope of the given line, $\tt{m=2}$

It passes through (6, 9)

The equation of the line is

$\tt{y-9=2(x-6)}$

$\tt{\implies\,y-9=2x-12}$

$\tt{\implies\,y=2x-12+9}$

$\tt{\implies\,y=2x-3}$

Answer 2

Given,

The given coordinates$\[ = \left( {6,9} \right)\]$

The slope of the line$\[ = 2\]$

To find,

The equation of the line.

Solution,

Know that the equation of a line is given as $\[y - {y_1} = m\left( {x - {x_1}} \right).\]$

Apply values.

Therefore,

$\[\begin{array}{l} \Rightarrow y - \left( 9 \right) = 2\left( {x - \left( 6 \right)} \right)\\ \Rightarrow y - 9 = 2\left( {x - 6} \right)\\ \Rightarrow y - 9 = 2x - 12\end{array}\]$

Solve further,

$\[\begin{array}{l} \Rightarrow 2x - 12 - y + 9 = 0\\ \Rightarrow 2x - y - 3 = 0\end{array}\]$

Hence, the equation of the line is$\[2x - y - 3 = 0\]$.