Question

the lines u, v, and w contain the coordinates given below:
u: (-6,-9) and (8,19)
v: (6,0) and (-10,8)
w: (0,-4) and (2,0)
which of the following are parallel?
a line v and line w
b line u and line v
c line u and line w
d line u, line v and line w

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: Calculate slope of line $u$

For line $u$ with points $(-6,-9)$ and $(8,19)$, $m_u=\frac{19-(-9)}{8 - (-6)}=\frac{19 + 9}{8+6}=\frac{28}{14}=2$.

Step3: Calculate slope of line $v$

For line $v$ with points $(6,0)$ and $(-10,8)$, $m_v=\frac{8 - 0}{-10 - 6}=\frac{8}{-16}=-\frac{1}{2}$.

Step4: Calculate slope of line $w$

For line $w$ with points $(0,-4)$ and $(2,0)$, $m_w=\frac{0-(-4)}{2 - 0}=\frac{4}{2}=2$.

Step5: Determine parallel lines

Two lines are parallel if they have the same slope. Since $m_u = m_w=2$, line $u$ and line $w$ are parallel.

Answer:

C. Line $u$ and line $w$