Question

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

Answer 1

Answer:

$_{\text{point-slope form}}$

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

$_{\text{slope-intercept form}}$

$\huge\boxed{y=-\dfrac{1}{4}x}$

Step-by-step 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

$m=-\dfrac{1}{4};\ (-4;\ 1)\to x_1=-4;\ y_1=1$

Substitute:

$y-1=-\dfrac{1}{4}(x-(-4))\\\\y-1=-\dfrac{1}{4}(x+4)$

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

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