Answer:
the equation of a line in slope intercept form of a line is
[tex]y=-\frac{1}{4}x-3[/tex] where [tex]m=\frac{-1}{4}[/tex].
Step-by-step explanation:
As the point-slope formula is
[tex]y-y_{1}=m(x-x_{1})[/tex]
So, the equation of a line with slope [tex]m=\frac{-1}{4}[/tex] and [tex]P(-4,-2)[/tex] will be
[tex]y-y_{1}=m(x-x_{1})[/tex]
[tex]y-\left(-2\right)=\frac{-1}{4}\left(x-\left(-4\right)\right)[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]y+2=\frac{-1}{4}\left(x+4\right)[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]y+2=-\frac{1}{4}\left(x+4\right)[/tex]
[tex]\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}[/tex]
[tex]y+2-2=-\frac{1}{4}\left(x+4\right)-2[/tex]
[tex]y=-\frac{1}{4}x-3[/tex]
As the slope intercept form of a line
[tex]y=mx+b[/tex]
Therefore, the equation of a line in slope intercept form of a line is
[tex]y=-\frac{1}{4}x-3[/tex] where [tex]m=\frac{-1}{4}[/tex].
Keywords: equation of a line , slope intercept form, slop
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