Question

If you know that A= 0 and B=0, how can you write an equation in point slope form of the equation Ax+By=C?

Answer 1

The equation of line in point slope form is given by

→$\frac{x}{a} + \frac{y}{b} =1$ , 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

→$\frac{x}{\frac{C}{A}}+\frac{y}{\frac{C}{B}}=1\\\frac{x}{0} +\frac{y}{0} =1$

→ 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.

     

Answer 2

We are given equation of line as

$Ax+By=C$

Firstly, we will solve for y

Subtract both sides by Ax

$Ax+By-Ax=-Ax+C$

$By=-Ax+C$

now, we can divide both sides by B

$y=-\frac{A}{B}x+ \frac{C}{B}$

now, we can write it in point slope form of line

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

so, we can get

$y-\frac{C}{B}=-\frac{A}{B}x+ \frac{C}{B}-\frac{C}{B}$

$y-\frac{C}{B}=-\frac{A}{B}x$

we can also write as

$(y-\frac{C}{B})=-\frac{A}{B}(x-0)$.............Answer