Answer:
[tex]_{\text{point-slope form}}[/tex]
[tex]\huge\boxed{y-1=-\dfrac{1}{4}(x+4)}[/tex]
[tex]_{\text{slope-intercept form}}[/tex]
[tex]\huge\boxed{y=-\dfrac{1}{4}x}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m[/tex] - a slope
[tex](x_1 y_1)[/tex] - a point of a line
We have
[tex]m=-\dfrac{1}{4};\ (-4;\ 1)\to x_1=-4;\ y_1=1[/tex]
Substitute:
[tex]y-1=-\dfrac{1}{4}(x-(-4))\\\\y-1=-\dfrac{1}{4}(x+4)[/tex]
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[tex]y-1=-\dfrac{1}{4}(x+4)\qquad|\text{use the distributive property}\\\\y-1=-\dfrac{1}{4}x-1\qquad|\text{add 1 to both sides}\\\\y=-\dfrac{1}{4}x[/tex]
