Question

what is the equation of the line that passes through the points $(-4, 1)$ and $(4, -1)$?
$y = -4x + 1$
$y = \frac{-1}{4}x$
$y = -4x$
$y = \frac{-1}{4}x + 2$

Explanation:

Step1: Calculate slope m

Given points $(x_1,y_1)=(-4,1)$ and $(x_2,y_2)=(4,-1)$, use slope formula:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-1}{4-(-4)}=\frac{-2}{8}=-\frac{1}{4}$$

Step2: Find y-intercept b

Use point-slope form $y-y_1=m(x-x_1)$ with $(-4,1)$:
$$y-1=-\frac{1}{4}(x-(-4))$$
Simplify:
$$y-1=-\frac{1}{4}x -1$$
$$y=-\frac{1}{4}x -1 +1$$
$$y=-\frac{1}{4}x$$

Step3: Verify with second point

Substitute $(4,-1)$ into $y=-\frac{1}{4}x$:
$$y=-\frac{1}{4}(4)=-1$$
This matches the given point.

Answer:

B. y = -1/4x