Question

a line passes through the points (1, -4) and (9, -4). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(1,-4)$ and $(x_2,y_2)=(9,-4)$:
$m=\frac{-4-(-4)}{9-1}=\frac{0}{8}=0$

Step2: Find y-intercept

Use slope-intercept form $y=mx+b$, substitute $m=0$ and $(x,y)=(1,-4)$:
$-4=0\times1+b$
Solve for $b$: $b=-4$

Step3: Write final equation

Substitute $m=0$ and $b=-4$ into $y=mx+b$:
$y=0x-4$ which simplifies to $y=-4$

Answer:

$y=-4$