We are given equation of line as
[tex]Ax+By=C[/tex]
Firstly, we will solve for y
Subtract both sides by Ax
[tex]Ax+By-Ax=-Ax+C[/tex]
[tex]By=-Ax+C[/tex]
now, we can divide both sides by B
[tex]y=-\frac{A}{B}x+ \frac{C}{B}[/tex]
now, we can write it in point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
so, we can get
[tex]y-\frac{C}{B}=-\frac{A}{B}x+ \frac{C}{B}-\frac{C}{B}[/tex]
[tex]y-\frac{C}{B}=-\frac{A}{B}x[/tex]
we can also write as
[tex](y-\frac{C}{B})=-\frac{A}{B}(x-0)[/tex].............Answer
The equation of line in point slope form is given by
→[tex]\frac{x}{a} + \frac{y}{b} =1[/tex] , where a and b are X intercept and Y intercept respectively.
The given equation is , Ax + B y -C=0 and we have to write it in point slope form, when x=0. and y=0 is
→[tex]\frac{x}{\frac{C}{A}}+\frac{y}{\frac{C}{B}}=1\\\frac{x}{0} +\frac{y}{0} =1[/tex]
→ Not defined + Not defined=1 or x+y=∞ which is not possible.
Or, when x=0,and y=0,
L.H.S= A×0 +B×0=0
R.H.S=C if C≠0 ,which is a real number.
If C=0, then→ x+y=0, which is slope intercept form when A=B=C=0.
L.H.S ≠ R.H.S
So, there is no line or no line can be written in slope intercept form when ,y=0 and x=0.
