Question

one line passes through points a and b. another line passes through points c and d. classify the lines as parallel, perpendicular, or neither.
a(-3,7), b(-6,0)
c(0,1), d(7,-2)
show your work here
parallel
perpendicular
neither

Explanation:

Step1: Calculate slope of line AB

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(-3,7)$ and $B(-6,0)$, we have $m_{AB}=\frac{0 - 7}{-6-(-3)}=\frac{-7}{-3}=\frac{7}{3}$.

Step2: Calculate slope of line CD

For points $C(0,1)$ and $D(7,-2)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_{CD}=\frac{-2 - 1}{7 - 0}=\frac{-3}{7}$.

Step3: Check relationship between slopes

Two lines are parallel if their slopes are equal, and perpendicular if the product of their slopes is - 1. Here, $m_{AB}
eq m_{CD}$ and $m_{AB}\times m_{CD}=\frac{7}{3}\times\frac{-3}{7}=- 1$.

Answer:

Perpendicular