Question

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

slope = -1/4

Answer 1

`_{\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`