Question

what is the equation of the line that passes through the points $(-4, 0.5)$ and $(4, -0.5)$?
$\bigcirc$ $y = -8x - 17$
$\bigcirc$ $y = \frac{-1}{8}x + 1$
$\bigcirc$ $y = -8x$
$\bigcirc$ $y = \frac{-1}{8}x$

Explanation:

Step1: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Let $(x_1,y_1)=(-4,0.5)$ and $(x_2,y_2)=(4,-0.5)$
$m=\frac{-0.5-0.5}{4-(-4)}=\frac{-1}{8}$

Step2: Find y-intercept $b$

Use point-slope form $y=mx+b$, substitute $m=-\frac{1}{8}$ and $(x_1,y_1)=(-4,0.5)$
$0.5 = -\frac{1}{8}(-4)+b$
$0.5 = 0.5 + b$
$b=0.5-0.5=0$

Step3: Write line equation

Substitute $m=-\frac{1}{8}$ and $b=0$ into $y=mx+b$
$y=-\frac{1}{8}x$

Answer:

D. $y = -1/8x$