Find the line passing through the given point and making the given angle with the given line. (2, 1), π/4, 2x – 3y + 2 = 0

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- Jun 10th 2012, 11:06 PM #1

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- Jun 10th 2012, 11:14 PM #2
## Re: please help me

The first line can be written as $\displaystyle \displaystyle \begin{align*} y = \frac{2}{3}x + \frac{2}{3} \end{align*}$, which has a gradient of $\displaystyle \displaystyle \begin{align*} \frac{2}{3} \end{align*}$.

You should know that the gradient $\displaystyle \displaystyle \begin{align*} m_1 \end{align*}$ makes the line make an angle $\displaystyle \displaystyle \begin{align*} \theta_1 \end{align*}$with the positive x axis, such that $\displaystyle \displaystyle \begin{align*} \tan{\theta_1} = m \end{align*}$. So from this line we can see

$\displaystyle \displaystyle \begin{align*} \tan{\theta_1} &= \frac{2}{3} \\ \theta_1 &= \tan^{-1}\left(\frac{2}{3}\right) \\ \theta_1 &\approx 0.588 \end{align*}$

You should also know that if you have two lines and know the angles they make with the positive x axis, then the angle between them $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$ can be evaluated by $\displaystyle \displaystyle \begin{align*} \theta = \theta_2 - \theta_1 \end{align*}$.

You have $\displaystyle \displaystyle \begin{align*} \theta \end{align*}$, you have $\displaystyle \displaystyle \begin{align*} \theta_1 \end{align*}$. Can you evaluate $\displaystyle \displaystyle \begin{align*} \theta_2 \end{align*}$ and use this to find the gradient of the line you are trying to find the equation of? From there can you find the equation of the line?