Question

Derive the equation of the straight line passing through the point $({x_1},{y_1})$ and having the slope $'m'$.

Answer 1

First we have to define what the terms we need to solve the problem are.
General solution of the given problem of a straight line is $y = mx + c$ and passing through the point $({x_1},{y_1})$ and the slope having is $'m'$.

Complete step by step answer:
We are going to use a formula of the equation of a straight line; $y = mx + c$ where, $m$ is the slope of the straight line and $c$ is the $y -$intercept.
Since given that a straight line is passing through the point $({x_1},{y_1})$ and having the slope $'m'$.
And equation of a straight line is given by $y = mx + c$, thus the point $({x_1},{y_1})$ satisfies $y = mx + c$ as it passes through the points, we get $\Rightarrow {y_1} = m{x_1} + c$.
(New axis points) Rewriting the equation, we have $\Rightarrow c = {y_1} - m{x_1}$ $(1)$
Substituting equation $(1)$ in equation $y = mx + c$, we get $\Rightarrow y = mx + {y_1} - m{x_1}$
Rewriting the equation, we get $y - {y_1} = m(x - {x_1})$
The equation of the straight line passing through the point $({x_1},{y_1})$ is $y - {y_1} = m(x - {x_1})$

Additional information: By using the two-point formula, we desire the equation of a straight line, which is of degree one (because it is linearly) and A line is simply an object in geometry zero width object that extends on both sides. A straight line has no curve lines.

Note: We can consider two point say $(x,y)$ and $({x_1},{y_1})$ and having the slope will be$m$,${m_1}$ because it has two axis points. Here, we have to derive the equation of a straight line. This can be derived using the one point and one slope formula. This derived equation can also be used to find the equation of the straight line. We can derive the same equation using the slope with two-point formula.