Question

determine whether the three points are collinear.
(0, - 9), (- 3, - 14), (2, - 5)

are the three points collinear?
no
yes

Explanation:

Step1: Calculate slope between first two points

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,-9)$ and $(x_2,y_2)=(-3,-14)$. Then $m_1=\frac{-14 - (-9)}{-3-0}=\frac{-14 + 9}{-3}=\frac{-5}{-3}=\frac{5}{3}$.

Step2: Calculate slope between second and third points

Let $(x_1,y_1)=(-3,-14)$ and $(x_2,y_2)=(2,-5)$. Then $m_2=\frac{-5-(-14)}{2 - (-3)}=\frac{-5 + 14}{2+3}=\frac{9}{5}$.

Step3: Compare slopes

Since $m_1=\frac{5}{3}$ and $m_2=\frac{9}{5}$, and $m_1
eq m_2$.

Answer:

No