Question

a line passes through the points (-1, -8) and (1, 6). 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 $(x_1,y_1)=(-1,-8)$ and $(x_2,y_2)=(1,6)$:
$m=\frac{6-(-8)}{1-(-1)}=\frac{14}{2}=7$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=7$ and $(x,y)=(1,6)$:
$6=7(1)+b$
Solve for $b$: $b=6-7=-1$

Step3: Write final equation

Substitute $m=7$ and $b=-1$ into $y=mx+b$.

Answer:

$y=7x-1$