Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts.

Solution:

(i) The given equation is $x+7 y=0$.

It can be written as

$y=-\frac{1}{7} x+0$ $\ldots(1)$

This equation is of the form $y=m x+c$, where $m=-\frac{1}{7}$ and $c=0$.

Therefore, equation $(1)$ is in the slope-intercept form, where the slope and the $y$-intercept are $-\frac{1}{7}$ and 0 respectively.

(ii) The given equation is $6 x+3 y-5=0$.

It can be written as

$y=\frac{1}{3}(-6 x+5)$

$y=-2 x+\frac{5}{3}$ $\ldots(2)$

This equation is of the form $y=m x+c$, where $m=-2$ and $c=\frac{5}{3}$.

Therefore, equation ( 2 ) is in the slope-intercept form, where the slope and the $y$-intercept are-2 and $\frac{5}{3}$ respectively.

(iii) The given equation is $y=0$.

It can be written as

$y=0 \cdot x+0$ $\ldots(3)$

This equation is of the form y = mx + c, where m = 0 and c = 0.

Therefore, equation (3) is in the slope-intercept form, where the slope and the y-intercept are 0 and 0 respectively.