Question

one line passes through the points (-8,1) and (4,4). another line passes through points (-9,-7) and (9,-3). are the lines parallel, perpendicular, or neither? choose 1 answer: a parallel b perpendicular c neither

Explanation:

Step1: Calculate slope of first line

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For the points $(-8,1)$ and $(4,4)$, we have $m_1=\frac{4 - 1}{4-(-8)}=\frac{3}{12}=\frac{1}{4}$.

Step2: Calculate slope of second line

For the points $(-9,-7)$ and $(9,-3)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_2=\frac{-3-(-7)}{9 - (-9)}=\frac{4}{18}=\frac{2}{9}$.

Step3: Check relationship between slopes

Two lines are parallel if $m_1 = m_2$, and perpendicular if $m_1\times m_2=- 1$. Since $\frac{1}{4}
eq\frac{2}{9}$ and $\frac{1}{4}\times\frac{2}{9}=\frac{1}{18}
eq - 1$.

Answer:

C. Neither