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?

The equation of the line in point slope form when y and x = 0 is:_______

Answer 1

The equation of line in point slope form is given by

→
`(x)/(a) + (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

→
`(x)/((C)/(A))+(y)/((C)/(B))=1\\(x)/(0) +(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=-(A)/(B)x+ (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-(C)/(B)=-(A)/(B)x+ (C)/(B)-(C)/(B)`

`y-(C)/(B)=-(A)/(B)x`

we can also write as

`(y-(C)/(B))=-(A)/(B)(x-0)`.............Answer