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Write the equation of the line that passes through the given point and has the given slope. (-4,1)

slope = -1/4

1 Answer

5 votes

Answer:


_{\text{point-slope form}}


\huge\boxed{y-1=-(1)/(4)(x+4)}


_{\text{slope-intercept form}}


\huge\boxed{y=-(1)/(4)x}

Explanation:

The point-slope form of an equation of a line:


y-y_1=m(x-x_1)

where


m - a slope


(x_1 y_1) - a point of a line

We have


m=-(1)/(4);\ (-4;\ 1)\to x_1=-4;\ y_1=1

Substitute:


y-1=-(1)/(4)(x-(-4))\\\\y-1=-(1)/(4)(x+4)

=============================================


y-1=-(1)/(4)(x+4)\qquad|\text{use the distributive property}\\\\y-1=-(1)/(4)x-1\qquad|\text{add 1 to both sides}\\\\y=-(1)/(4)x

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