Question

Find the equation of a line passing through $(4,8)$ and equally inclined to the coordinate axes in the first quadrant.

Answer 1

Step 1:Finding the slope of the line:

Given that the line is equally inclined to the coordinate axes in the first quadrant

Thus , the line is making $45°$ angle with both axes.

The slope of the line making an angle $\theta$ with$X-axis$ is given as:

$m=\tan \theta$

Then ,the slope of the line making an angle $45°$ with$X-axis$ is given as

$$\begin{gathered} m=\tan 45° \\ m=1 \end{gathered}$$

Hence slope of the line is $1$.

Step 2:Finding the equation of a line:

Equation of line passing through point $\left(x_1,y_1\right)$ and having slope $m$ is given as

$y-y_1=m\left(x-x_1\right)$

Equation of line passing through point $(4,8)$ and having slope $1$ is given as:

$\begin{array}{rcl}y-8& =& 1\left(x-4\right)\\ y-8& =& x-4\\ x-y-4+8& =& 0\\ x-y+4& =& 0\end{array}$

Therefore, the required equation of a line is $\begin{array}{rcl}x-y+4& =& 0\end{array}$