Question

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

Answer 1

Given a line passing through $(x_1,y_1)$ having slope 'n' then

Let equation of line can be written as

y=kx+c ________ (1)

Where k= slope C= constant

$(x_1,y_1)$ satisfy equation (1) as it passes through points then

$y_1=m{x}_1+c$

$c=y_1-m{x}_1$ ________ (2)

using equation (2) in (1) we get

$y=mx+y_1-m{x}_1$

$y-y_1=m(x-x_1)$ ___________ (3)

Hence equation (3) is required equation of line.