Question

$1)$ Reduce the following equations into slope-intercept form and find their slopes and the $y$-intercepts.
$\left(i\right)$ $x+7y=0$

$2)$ Reduce the following equations into slope-intercept form and find their slopes and the $y$-intercepts.
$\left(ii\right)$ $6x+3y-5=0$

$3)$ Reduce the following equations into slope-intercept form and find their slopes and the $y$-intercepts.
$\left(iii\right)$ $y=0$

Answer 1

$1)$ Intercept form

Given $x+7y=0$

$\Rightarrow 7y=0-x$

$\Rightarrow 7y=-x$

$\Rightarrow y=\frac{-x}{7}$

$\Rightarrow y=\frac{-x}{7}+0$

$\Rightarrow y=-\frac{1}{7}x+0$

This equation is in the form

$y=mx+c$

Hence, slope $m=-\frac{1}{7}$

& $y-\text{intercept}=c=0$

$2)$ Intercept form

Given $6x+3y-5=0$

$\Rightarrow 3y=-6x+5$

$\Rightarrow y=\frac{-6x+5}{3}$

$\Rightarrow y=\frac{-6x}{3}+\frac{5}{3}$

$\Rightarrow y=-2x+\frac{5}{3}$

This equation is in the form $y=mx+c$

Hence, slope $m=-2$

& $y$ intercept $c=\frac{5}{3}$

$3)$ Intercept form

Given $y=0$

This can be written as

$y=0x+0$

This equation is of the form $y=mx+c$

Hence, slope $m=0$

& $y-\text{intercept}c=0$