Question

a line passes through the points (-1, 10) and (4, -10). 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 $(x_1,y_1)=(-1,10)$ and $(x_2,y_2)=(4,-10)$.
$m=\frac{-10-10}{4-(-1)}=\frac{-20}{5}=-4$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=-4$ and $(-1,10)$:
$10 = -4\times(-1)+b$
$10=4+b$
$b=10-4=6$

Step3: Write final equation

Substitute $m=-4$ and $b=6$ into $y=mx+b$.
$y=-4x+6$

Answer:

$y=-4x+6$