Question

a line passes through the points (-19, 17) and (17, -19). 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 $m=\frac{y_2-y_1}{x_2-x_1}$. Let $(x_1,y_1)=(-19,17)$ and $(x_2,y_2)=(17,-19)$.
$m=\frac{-19-17}{17-(-19)}=\frac{-36}{36}=-1$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=-1$ and $(x,y)=(-19,17)$.
$17 = -1\times(-19)+b$
$17=19+b$
$b=17-19=-2$

Step3: Write final equation

Substitute $m=-1$ and $b=-2$ into $y=mx+b$.

Answer:

$y=-x-2$