Reduce the following equations into slope intercept form and find their slopes and the y intercepts.(i) $x+7y=0$, (ii) $6x+3y5=0$, (iii) $y=0$.

Solution: Slope-intercept form can be given as,
$y=mx+c$, where $m$ is slope and $c$ is y-intercept.

(i) $x+7y=0$
$\Rightarrow 7y=-x+0$
$\Rightarrow y=\left(-\frac{1}{7}\right)x+0$
$\therefore$ Slope is $-\frac{1}{7}$ and y-intercept is $0$.

(ii) $6x+3y-5=0$
$\Rightarrow 3y=-6x+5$
$\Rightarrow y=-2x+\frac{5}{3}$
$\therefore$ Slope is $-2$ and y-intercept is $\frac{5}{3}$.

(iii) $y=0$
$\Rightarrow y=0x+0$
$\therefore$ Slope is $0$ and y-intercept is $0$.