Question

what is the slope of line pq?
what is the slope of line mn?
how are the two lines related?
the lines are parallel.
the lines are perpendicular.
the lines do not have slope.
the lines are not coplanar.

Explanation:

For the slope of line PQ:

Step1: Identify coordinates of P and Q

Point P is at \((-8, 2)\) and point Q is at \((4, 2)\).

Step2: Use slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substitute \(x_1=-8\), \(y_1 = 2\), \(x_2 = 4\), \(y_2=2\) into the formula:
\(m_{PQ}=\frac{2 - 2}{4 - (-8)}=\frac{0}{12}=0\)

For the slope of line MN:

Step1: Identify coordinates of M and N

Point M is at \((8, 6)\) and point N is at \((8, -8)\).

Step2: Use slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

Substitute \(x_1 = 8\), \(y_1=6\), \(x_2 = 8\), \(y_2=-8\) into the formula:
\(m_{MN}=\frac{-8 - 6}{8 - 8}=\frac{-14}{0}\), which is undefined (vertical line has undefined slope).

For the relationship between the two lines:

A horizontal line (slope 0) and a vertical line (undefined slope) intersect at right angles (90 degrees), so they are perpendicular.

Answer:

s:

• Slope of line PQ: \(0\)
• Slope of line MN: Undefined
• Relationship: The lines are perpendicular. (Option: The lines are perpendicular.)