I know,
$Ax + By = C$
is the equation of straight line but a different resource says that:
$y = mx + b$
is also an equation of straight line? Are they both same?
I know,
$Ax + By = C$
is the equation of straight line but a different resource says that:
$y = mx + b$
is also an equation of straight line? Are they both same?
Yes. That is, they both give the equation of a straight line and the equation of any non-vertical line can be written in either form.
If $B\ne 0$. Then you can write $Ax+By=C$ as $ By=-Ax+C $ and, since $B\ne0$, the above can be written $ y=-\textstyle{A\over B}x +{C\over B}. $
If $B=0$, the equation is $Ax=C$, which is a vertical line when $A\ne0$. In this case you can't write it in the form $y=mx+b$ (which defines a function).
On the other hand, given $y=mx+b$, you can rewrite it as $-mx+y=b$.
The $y$-intercept of its graph is $C/B$ and is found by taking $x=0$.
The $x$-intercept is of its graph is $C/A$ and is found by taking $y=0$.
The slope of the line is then $ {C/B-0\over 0-C/A } = -A/B$.
$Ax + By = C$
$By = -Ax + C$
$y = -(A/B)x + C/B$
Let $m = -\frac{A}{B}$. Let $b = \frac{C}{B}$.
$y = mx + b$
So they are equivalent.