Question

reduce the equation root 3x+y+2=0 to 1)slope intercept form 2)intercept form and 3) normal form

Answer 1

Given line is 3x+y+2=0

1.Slope-Intercept form:

$3x+y+2=0$

$\implies\,y=-3x-2$

$\implies\,y=-3x+(-2)$

$\textbf{This equation is of the form y=mx+c}$

$\implies\;m=-3\:\:and\:\:c=2$

2.Intercept form:

$3x+y+2=0$

$3x+y=-2$

Divide bothsides by -2

$\frac{3x}{-2}+\frac{y}{-2}=1$

$\frac{x}{-2/3}+\frac{y}{-2}=1$

$\text{This equation is of the form }\bf\frac{x}{a}+\frac{y}{b}=1$

$\implies\;a=-2/3\:\:and\:\:b=-2$

3.Normal form:

$3x+y+2=0$

$-3x-y=2$

Divide both sides by $\sqrt{9+1}=\sqrt{10}$, we get

$\frac{-3}{\sqrt{10}}x+\frac{-1}{\sqrt{10}}y=\frac{2}{\sqrt{10}}$

$\text{This equation is of the form }\bf\,x\:cos\alpha+y\:sin\alpha=p$

$\implies\,\alpha=cos^{-1}(\frac{-3}{\sqrt{10}})=sin^{-1}(\frac{-1}{\sqrt{10}})\:\:and\:\:p=\frac{2}{\sqrt{10}}$