Question

a line passes through the points (-7, -4) and (7, 0). 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 $(x_1,y_1)=(-7,-4)$ and $(x_2,y_2)=(7,0)$.
$m=\frac{0-(-4)}{7-(-7)}=\frac{4}{14}=\frac{2}{7}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=\frac{2}{7}$ and point $(7,0)$:
$0=\frac{2}{7}(7)+b$
$0=2+b$
$b=-2$

Step3: Write final equation

Substitute $m=\frac{2}{7}$ and $b=-2$ into $y=mx+b$.

Answer:

$y=\frac{2}{7}x-2$