Question

Find the equation of the line passing through the point $(2,3)$ and having slope $3$.

Answer 1

Finding the equation of a line:

Given that the line is passing through $(2,3)$, then

$x_1=2and{y}_1=3$

Slope the line ( $m$) is $3$

Equation of a line through any point $(x_1,y_1)$ and having slope $m$ is given as:

$y-y_1=m(x-x_1)$

Equation of line passing through $(2,3)$ and having slope of line as $3$ is given as:

$\begin{array}{rcl}y-3& =& 3(x-2)\\ y-3& =& 3x-6\\ 3x-6+3-y& =& 0\\ 3x-y-3& =& 0\end{array}$

Hence required equation is $\begin{array}{rcl}3x-y-3& =& 0\end{array}$