Question

write an equation of the line below.

Explanation:

Step1: Identify two points

The line passes through $(-5, 7)$ and $(1, 3)$.

Step2: Calculate the slope

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{3-7}{1-(-5)}=\frac{-4}{6}=-\frac{2}{3}$

Step3: Find y-intercept (b)

Substitute $m=-\frac{2}{3}$ and $(1,3)$ into $y=mx+b$:
$3=-\frac{2}{3}(1)+b$
$3+\frac{2}{3}=b$
$b=\frac{11}{3}$

Step4: Write line equation

Substitute $m$ and $b$ into $y=mx+b$

Answer:

$y=-\frac{2}{3}x+\frac{11}{3}$